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3D Convolutional Neural Network (3D CNN) — A guide for engineers

Key takeaways

  • A 3D CNN is a neural network architecture that takes a solid object as input, such as a CAD geometry or a CT scan.
  • The geometry enters the network directly, as exported from the CAD system.
  • Trained on past simulations, it returns quantities such as drag or surface temperature in seconds.
  • Accuracy follows the training simulations: their coverage of the design space counts more than their number.
Table of contents

A 3D Convolutional Neural Network (3D CNN) is a deep learning architecture that extends the concept of pattern recognition from two-dimensional data to three-dimensional inputs. Instead of processing data in height and width only (as 2D CNNs do), 3D CNNs operate on height × width × depth (the input volume), making them ideal for volumetric data (e.g., CT scans, CAD models, CFD simulations) or image time series (video). This added depth dimension allows the network to detect patterns and correlations across multiple slices or frames, enabling engineers to extract richer and more context-aware features for tasks such as simulation acceleration, defect detection, and complex product design.

Artificial Intelligence (AI) and Deep Learning (DL) have revolutionized how we approach engineering problems. The revolution took off in computer vision and speech recognition; now it is spreading to product design. One of the most exciting advances in DL is the Convolutional Neural Network (ConvNet). Recent research has opened the way for implementing even a 3D Convolutional Neural Network. 3D CNNs are key enablers for the revolution in engineering, empowering product design engineers with high-end simulation capability. So, 3D CNNs are an extension of traditional Convolutional Neural Networks, designed to handle data with spatial dimensions including height, width, and depth.

Illustrated engineer next to a board showing a CNN pipeline and a convolution kernel sliding over a pixel grid

This guide explains how 3D CNNs drive business value in engineering, starting with an automotive case.

We will explain the basic concepts of this technology for readers without an AI background, then progress to advanced applications, including training and validation sets, as well as model building. The goal is to understand how neural networks enable AI to “learn” 3D CAD shapes.

The objective is to build predictive models that forecast engineering behavior, such as aerodynamics, from data. Mastering this technology positions engineers to drive measurable impact in product design.


Preliminary case history: better competition with 3D convolutional neural networks

Tier 1 automotive suppliers now win by offering more design options, not just solving problems. The advantage comes from shifting to proactive exploration, powered by 3D CNN-based predictive models.

Two challenges remain with traditional high-fidelity simulation:

  • First: make simulation accessible to every engineer, without requiring specialized infrastructure or training.
  • Second: enable every engineer to explore multiple design options, not just a select few.

Early predictive capability, deployed across R&D, design, and sales, creates a measurable edge in RFQs and customer engagement.

The next step: deploy tools that demonstrate product innovation, cost-effectiveness, and compliance with performance requirements.

How to support product design

Product design advances fastest when engineering expertise is paired with data-driven tools that predict performance and verify compliance before manufacturing begins.

The challenge: demonstrate compliance with targets and constraints before manufacturing starts.

Three approaches exist:

  1. First: copy previous designs. This fails in the long term due to performance gaps and regulatory risk.
  2. Second: rely on testing, prototyping, and CAE. This is slow and resource-intensive.
  3. Third: use deep learning to build predictive models from past solutions. This enables rapid, real-time demonstration of product capabilities.

With real-time prediction in place, the next step is iterative design (automated or generative) to achieve targets like lower weight, improved heat dissipation, and higher energy efficiency.

Can my company use AI to predict designs?

AI-driven simulation for product design is accessible and practical.

Two requirements: a business case and relevant data.

  • A business case is simply the need to be competitive and innovative to attract customers or prospects
  • Data are generated whenever your company designs CAD and performs CAE simulation or testing

For instance, you must deliver a product in 8 weeks instead of 6 months. That’s your business case. And you have data from the last 2 years, during which you’ve developed 4 product concepts, with their simulated variants, to train your AI. As for how much data, coverage and quality matter more than raw volume: a smaller, representative dataset can outperform a larger but poorly curated one when combined with robust data collection and management practices for AI models.

In the following, we will provide a more detailed explanation of how prediction arises from data, particularly for 3D engineering data. Physics-based prediction from 3D geometry is one of the core capabilities of the Neural Concept platform. It enables CAE engineers and data scientists to build fast predictive models and deploy them across design teams. More broadly, Neural Concept combines this capability with design space generation, simulation automation, and AI-powered co-pilots, giving engineering organizations the tools to make every design decision faster and more data-driven.

Why 3D convolutional neural networks matter for engineers

3D CNNs deliver higher accuracy and performance than traditional models. The result: competitive advantage and increased market share.

Please note that the following technical details are intended to satisfy your curiosity about the inner workings of Deep Learning tools such as the Neural Concept platform. Still, we assure you that using the Neural Concept platform for AI-assisted engineering prediction requires no prerequisite skills in AI, data science, or computer science.

We review how 3D CNNs work, covering classification, regression, and architecture. Then we detail their core building blocks.


Learning – in humans and artificial agents

We will first give an overview of the AI training process, a key passage towards an actionable AI for designers.

There are three main types of AI learning. We will focus on supervised training, i.e., training with labeled data to predict labels for new examples.

Two other approaches are

  • unsupervised training (finding patterns in unlabeled data) and
  • reinforcement training (training through interaction with an environment).

A model is trained to perform a task using labeled examples in supervised learning. This process can occur with humans and artificial intelligence (AI) systems. The differences between human and artificial training can provide insight into the strengths and limitations of AI. Let’s use image classification for supervised training; in this task, the deep learning model is trained to identify the class of an image (e.g., dogs, cats, etc.) based on labeled examples.

What about humans?

Training humans

Humans learn through experience and observation, recognizing objects in images by repeated exposure to labeled examples. From early childhood, this process involves real objects and verbal interaction. It is time-consuming and memory-intensive, but humans benefit from understanding context and applying prior knowledge to identify objects in new images.

experience and observation are fundamental in human training

Introduction to deep learning training

Deep learning systems can perform tasks much faster and more efficiently than humans. However, they are trained to perform specific tasks without truly understanding the meaning or context of their actions. We aim to automate engineering tasks that can be easily translated into mathematical models and to extract data from past experiences, such as design, laboratory testing, and CAE simulations.

It’s important to recognize that deep learning techniques have certain limitations. Unlike humans, these systems do not understand the context and meaning of images. Instead, they use the features and characteristics they’ve learned from labeled examples to make predictions. This means they may not generalize well when evaluated on unseen data or other new images.

Technical aspects of DL training

Deep learning (DL) systems can be trained on large datasets of labeled images to quickly learn the features of each object class. The process involves adjusting mathematical connections, called “weights,” in the model (a neural network). This minimizes the error between predicted and actual class labels using algorithms such as gradient descent, enabling the DL system to learn much faster than a human could.

Predicting with DL

Deep learning systems can make predictions much faster than humans, achieving superhuman performance. For instance, they can process images and produce classification results in real time, whereas a person would need far longer to identify each image. In a multi‑class classification problem, the model assigns a probability to each possible category and selects the one with the highest score.

When dealing with video files, practical pipelines often preprocess video data before evaluation, and the model then evaluates video sequences across frames and aggregates the results to classify the entire sequence. This allows recognition of actions, events, or objects across thousands of frames within seconds, making it a strong fit for video analysis.

3D CNNs have improved action recognition on benchmark video datasets such as UCF101 and are increasingly central to deep learning applications in engineering and beyond.

The speed advantage of DL is particularly evident with complex industrial designs. Predicting the surface temperature of a complex industrial geometry under its operating conditions is precisely the type of data-driven engineering prediction that the Neural Concept platform specializes in. Such predictions are known as regression.

Prediction & regression speed

The challenge may not be about classification but about regression, i.e., predicting a number, such as in the following question: what is the aerodynamic coefficient of this car, given its 3D geometry?

What is the aerodynamic performance of this car, including pressure and velocity around and on its body, to calculate drag and downforce?

The answer can be obtained via

  1. traditional software (CFD) simulating fluid mechanics and turbulence, or
  2. AI trained on such data to predict values based on geometry. The AI approach can achieve greater speed than physics-based software written by humans. 3D CNN predictions can be several orders of magnitude (from 1,000 to 1,000,000) faster than traditional computational software, such as CAE, which relies on physical knowledge of aerodynamics and industrial geometries, such as cars, a speedup exemplified by AI-driven aerodynamic prediction on the DrivAerNet++ benchmark.

What are classification and regression?

Classification and regression are two common types of supervised machine learning (ML). More precisely, in a classification task, the goal is to predict a categorical label for a given input data. In a regression task, the goal is to predict a continuous value for a given input.

Practical examples: cats vs dogs & house prices

Let’s start with a simple example to understand the difference between classification and regression. Imagine you have a dataset of images of cats and dogs, and you want to train an ML model to predict whether each image is a cat or a dog. This is a classification task where the output is a label (“cat” or “dog”). The input is the image, and the output is a binary label (“0” for cat, “1” for dog). The model learns patterns, like fur and whiskers, to predict the label.

Now, consider a dataset of housing prices. You want to predict a house’s price based on size, number of bedrooms, and number of bathrooms. This is a regression task with a continuous output. The input is the features, and the output is the house price. The model learns patterns, like larger size and more rooms, to predict prices.

Classification and regression in ML

In supervised ML, tasks are typically split into two main types: classification, which predicts discrete categories, and regression, which predicts continuous numerical values. Both approaches train a model on labeled data to learn the mapping from inputs to outputs.

What is classification in machine learning?

Classification is a type of supervised learning that predicts a categorical label for a given input. Each sample belongs to exactly one class, which can be binary (e.g., cat or dog) or multi-class (e.g., red, green, blue).

The model is trained on a labeled dataset (pairs of input data and category labels) to learn how to map new inputs to the correct class.

Key evaluation metrics include:

  • Accuracy – proportion of correctly classified samples.
  • Precision – proportion of predicted positives that are correct.
  • Recall – proportion of actual positives correctly identified.
  • F1 score – harmonic mean of precision and recall.

A confusion matrix is often used to visualize performance, showing true positives, false positives, true negatives, and false negatives. Correct predictions appear on the diagonal; errors are in the off-diagonal cells.

What is regression in ML?

Regression is a type of supervised learning that predicts a continuous numerical value for a given input, such as temperature, fuel efficiency, or price.

The model is trained on a labeled dataset (pairs of input data and numerical targets) to learn the relationship between the features and the continuous output.

Key evaluation metrics include:

  • Mean Squared Error (MSE) – average squared difference between predictions and true values.
  • Mean Absolute Error (MAE) – average absolute difference between predictions and true values.
  • R-squared (R²) – proportion of variance in the target explained by the model.

A higher R² generally means a better fit. However, it must be interpreted with other diagnostics (e.g., residual plots) to detect overfitting or poor generalization.


Deep learning and 3D CNN architecture

A 3D CNN is a neural network architecture with multiple layers that can learn hierarchical data representations from data. Each layer learns increasingly complex features, building hierarchical data representations that capture richer spatial patterns over depth and time. These 3D CNNs can then be used for various tasks such as classification, regression, or generation. Each type of layer has a definite function. 3D CNNs process volumetric data, a core form of three-dimensional data, and are specifically designed to capture spatial and temporal dependencies. 3D CNNs utilize 3D convolutional layers that apply three-dimensional filters to scan the input data. For instance, 3D CNNs achieve higher accuracy in analyzing temporal relationships in video data than 2D CNNs, which treat video frames as separate images, though 3D CNNs require greater computational resources. Some architectures factorize 3D convolutions into separate spatial and temporal steps. The (2+1)D convolution keeps the number of parameters of the full 3D convolution and adds a nonlinearity between the two steps.

Example layers in a 3D CNN

For example, the max-pooling layer is a “downsampler” for feature maps. In 3D CNNs, pooling layers placed after the 3D convolutional layers typically reduce the size of feature maps and operate in three dimensions.

A feature map is generated by convolving a filter over an image; pooling then reduces its spatial size and computational burden. Another form of pooling is global average pooling.

Intuitive illustration of the workings in a max pooling layer; only maximum values are kept in each area

How neural networks learn

A neural network consists of interconnected processing nodes, artificial neurons. Let’s have a deeper look at the connection between neurons and learning. How can they possibly learn? The key to the approach shown here (supervised learning) is to have examples to learn from.

In DL, neurons are organized into layers (this is the “depth” of DL).

Neurons in the first layer process the input, and the output from one layer serves as input to the next, and so on until the final layer’s output reasonably represents the prediction.

Furthermore, each layer is trained to learn hierarchical data representations progressively, from simple patterns to more complex ones. For example, in image classification, the first layer may learn to recognize edges and basic shapes, and the next layer may learn to recognize more complex shapes, and so on, until the input reaches the final layer. It transforms into a high-level representation for image prediction or classification.

How does training work?

The weights of neurons in DL neural networks are trained using backpropagation. Backpropagation updates the weights based on the error between the predicted output and the ground truth label. The error is propagated backward (hence the name backpropagation) through the network, and the weights are adjusted to reduce it.

This process is repeated until the error reaches an acceptable level.

If ŷ is the prediction for a given input x, the error between the predicted output and the true label y is expressed by formulas such as:

E = (ŷ – y)²

The training process aims to minimize this error by adjusting the network’s weights and biases. The weights are optimized using algorithms such as gradient descent, which adjust them in the direction of the negative gradient of the error E.


What is the goal of deep learning?

Deep learning aims to build systems that create their own internal models of data rather than relying on rules defined by humans. Through training, millions of model parameters are adjusted. These models capture relationships in data that are too complex to specify manually. The objective is not to mimic how people learn, but to develop methods to solve problems for which explicit programming is impossible because the patterns are unknown or too numerous to enumerate.

3D CNNs: classification

3D CNNs are deep learning models used in various applications, such as computer vision or medical imaging. For instance, the application of 3D CNNs in medical imaging enables Medical Imaging Detection for tumors, lesions, and other abnormalities. In medical image segmentation, encoder-decoder architectures are commonly used in 3D CNN models to delineate organs and abnormalities in volumetric scans.

In these cases, we want AI to learn how to respond to inputs rather than to be programmed according to a predetermined pattern. The outcome of this learning process is a predictive model. The predictive models emerging from the 3D CNN framework are designed to process and analyze data with a temporal dimension, such as videos. 3D CNNs can be used to process 3D point cloud data from LiDAR sensors for object detection and semantic segmentation in robotics and autonomous vehicles.

Computer “vision” means that the 3D CNN can learn spatial relationships and patterns in the data and extract features for tasks such as classification or segmentation. The goal is to assign a semantic label, such as “road”, “building”, “vehicle”, etc., to each pixel in the image, providing a detailed understanding of the scene’s spatial information. A recent innovation is the use of a 3D convolutional neural network to associate accurate engineering predictions from simulation software with CAD designs and to quantify predictive uncertainty.

3D CNNs: regression

Earlier, we mentioned using a 3D CNN to associate accurate engineering predictions from simulation software with CAD designs.

If the 3D ConvNet is trained on CAD geometries associated with CFD results, it will perform a regression rather than a classification task. In this scenario, the input to the network would be the CAD geometry, and the output would be the corresponding CFD result.

The 3D ConvNet would learn to map the input CAD geometry to the output CFD result based on the training data. This could be useful for problems where the goal is to find the optimal CAD geometry, and performance is evaluated using CFD or its ConvNet predictive model.

The ConvNet predictive model works by extracting features from the input CAD geometry using 3D convolutions and processing these features through multiple layers to produce the final output. The network weights are updated during training to minimize the difference between the predicted and ground-truth CFD results.

Thus, it becomes possible to envisage (and achieve) very ambitious objectives, such as coupling the neural network’s regression capability to a geometric shape to optimize, leading to generative AI engineering (creating new shapes within the AI software without the need for third-party tools).


Training the neural network

During training, the network weights are updated to minimize the difference between the predicted and ground-truth CFD results using a loss (or error) function.

Training: loss functions

A common loss (or error) function used in regression tasks is the mean squared error (MSE) loss. The loss (error) measures the average squared difference between the predicted and ground-truth CFD results.

The goal of training is to minimize this value and is expressed as

Loss = (1/N) * Σᵢ (ŷᵢ – yᵍᵗᵢ)²

where

  • N is the number of samples in the training set,
  • ŷᵢ is the predicted CFD result for the iᵗʰ sample, and
  • yᵍᵗᵢ is the ground truth (“gt”) CFD result for the iᵗʰ sample.

The summation runs over the dummy index i for samples from 1 to N.

Regardless of the exact mathematical form, the network weights are updated using an optimization algorithm, such as stochastic gradient descent (SGD), to minimize the loss.

Training: loss gradient

The loss gradient is computed via backpropagation, enabling the network to update its weights in the direction that minimizes loss. The weight update rule for SGD is given by:

w‘ = w – η * ∇ Loss

where w is the weight, η is the learning rate, and ∇Loss is the loss gradient with respect to the weight.

The learning rate η determines the step size at which the weights are updated, and it is a hyperparameter that must be chosen carefully:

  • a high learning rate can cause the network to converge quickly, but it may not find the optimal solution
  • a low learning rate can provide a more accurate solution but may take longer to converge.

The building brick: the artificial neuron

The Artificial Neuron is the basic building block, a sort of “atom”, of Artificial Neural Networks (ANNs), which are modeled after the structure and function of biological neurons in the human brain.

ANNs are commonly described as computational models that simulate how the human brain processes information.

We restrict this ambitious definition to a more specific one: a useful ANN for engineers is “a computational model that reproduces some specific functions of the brain, or software produced by humans, used in engineering, to assist humans with superhuman speed“.

Model for the single physical neuron

The human brain is complex, processing vast amounts of information to facilitate interaction with its surroundings. Neurons, specialized cells transmitting information, are crucial. They receive and process sensory data and send signals via electrical and chemical means. Interconnected neurons form networks that process information in parallel, with connection strength influencing their likelihood of firing.

Mathematical models of neurons and neural networks have been developed to understand how the brain processes information. These models can predict neuronal responses to stimuli and reveal relationships among neurons. A simple mathematical model of a neuron is an artificial neuron consisting of inputs, weights, and an activation function that converts inputs into output.

Biological neuron compared with an artificial neuron: weighted inputs, sum and activation function

The artificial neuron

For our engineering purposes, artificial neurons serve as simplified models inspired by biological neurons, used as building blocks for complex functions such as human brain simulations and software. Perceptrons are mathematical functions that process inputs to produce outputs. We do not aim to replicate biological neurons precisely, just to use them as a basis for artificial learning.

Building blocks of the artificial neuron

Artificial Neurons have three components:

  • inputs x; they are the signals the neuron receives from other neurons in the network.
  • weights w; values that determine the strength of the input signals
  • and an activation function f, a mathematical operation that determines whether the neuron will fire, or generate an output signal y, based on the input signals x and weights w.

So we imagine something like

y=f(x, w, b)

where the bias term b could represent other parameters.

The inputs to an artificial neuron are multiplied by their corresponding weights, and the results are then summed.

Core operation in the artificial neuron

The artificial neuron mathematics can be represented as

z = w • x + b

where “b” is the bias term, and “z” is the resulting sum of all weighted inputs.

This weighted sum is passed through an activation function f, as mentioned above, which determines whether the neuron will generate an output signal y = f(z). This function is usually non-linear, such as a sigmoid or rectified linear unit (ReLU), allowing the network to model complex relationships between inputs and outputs.

The function can be a sigmoid function:

f(z) = 1 / (1 + e⁻ᶻ)

or a rectified linear unit (ReLU) function:

f(z) = max(0, z).

From a single neuron to a neural network

Artificial Neurons are the building blocks of ANNs and can be connected to form more complex models. For example, multiple artificial neurons can be connected to form a layer of a neural network, and multiple layers can be stacked to form a deep neural network. In a neural network, each neuron receives input from multiple neurons in the previous layer, and the output of each neuron in one layer serves as input to multiple neurons in the next layer.


Neural network training

Training a neural network involves adjusting its parameters to minimize the error between its predictions and the true outputs. The network is provided with input + output data called training data. The training aims to find the best parameters that enable the network to correctly predict the outputs for these data. This is achieved through ML algorithms, which adjust the parameters based on the difference between the predicted and actual outputs.

Neural network training data

More high-quality training data, with careful data preparation, is crucial for successfully training neural networks. More data means better learning, but data quality is important to avoid biased or noisy results. This process can be challenging, especially with large datasets, but it is essential. Balancing underfitting and overfitting is another challenge, where the network may be too simple or too complex, resulting in poor performance. Techniques like regularization, early stopping, and dropout can improve generalization and performance on new data.

Loss functions

Choosing the right function is a challenge when training a neural network. The appropriate loss depends on the problem being solved, such as mean squared error for regression, cross-entropy for classification, and hinge loss for binary classification. Data quality, the balance between underfitting and overfitting, choice of function, and the optimization algorithm all affect model performance.

ConvNet architecture: convolution, max-pooling and non-linear layers feeding fully connected layers that output ten classes

How does a 3D convolutional neural network work?

A 3D CNN is based on the concept of convolutional neural networks (CNNs) but adds a third axis, which may be temporal (as in video) or spatial (as in volumetric data).

In a traditional 2D CNN, the input is a single image with one or more channels, which the network processes and analyzes. In a 3D convolutional neural network, the input includes a third spatial or temporal dimension, enabling analysis of relationships between the slices of a volume or between frames over time.

Layers & feature maps

The 3D convolutional neural network architecture comprises several layers, including an input layer, multiple convolutional layers, activation functions, max-pooling layers, and a final classification layer, with convolutional layers learning from volumetric inputs and video sequences.

The convolutional layers learn and extract spatial and temporal features from the input, and some architectures factorize 3D convolutions into separate spatial and temporal components. Activation functions introduce non-linearity into the model, allowing it to model complex relationships between the input and the target output.

Feature maps are arrays of values that represent a specific feature in an image, such as an edge or a texture. The map is generated by applying convolutional filters to an input image. The filters scan the image and detect patterns at different scales, producing maps.

Max-pooling layers

“Max-pooling” reduces the size of the map by dividing it into non-overlapping regions (often squares) and taking the max value in each region. Max-pooling layers preserve important features in the map by retaining the maximum activation value within each region while reducing the size of the feature map, making the network more computationally efficient and helping manage computational load. Furthermore, reducing the feature map’s size helps the network become more robust to small translations in the input image, as the max-pooling operation is invariant to such translations.

Fully connected layers

The classification layer typically comprises one or more fully connected (dense) layers, each connected to every neuron in the previous layer. The predictions made by the classification layer are based on the features learned by the previous layers. These features can include edges, textures, and shapes. Thus, classification layers are a crucial component of a Convolutional Neural Network to make predictions based on the features learned by the network.


Convolution in detail

Convolution is a mathematical operation that allows information from one function to be transformed and combined with another. It is widely used in image processing, signal processing, and ML. Convolution can be represented mathematically using convolutional operators, which are functions that define the relationship between the input and output channels.

The mathematics of convolution

The convolution operation between signals f and g can be mathematically expressed as

(f*g)(t) = ∫ f(τ) g(t – τ) dτ,

where f and g are input signals, t is time, ∫ signifies an integral over time (with τ as the dummy variable of integration), and ‘*’ denotes the convolution operator.

The convolution ‘*’ generates an output signal, which is a transformed version of the input signals.

Application to image processing

In image processing, the input signals can be viewed as pixels, and the convolutional operator functions as a filter. This filter is applied to each region of the image, producing a transformed version that highlights specific features. Repeating this process with different convolutional filters allows the extraction of various image features. Convolution in image processing and ML offers many advantages over older methods.

Advantages of convolution

One major benefit is its ability to automatically extract features from the input, unlike traditional techniques that require manual feature extraction, a time-consuming, labor-intensive process. Additionally, convolution preserves the spatial structure of the input because it is applied locally, considering only a small region at a time. This is crucial for tasks like object recognition and image classification.

Convolutional layers in deep networks learn to identify the most relevant features within the input. These filters are adjusted during training to optimize model performance. Lastly, convolution is computationally efficient on modern hardware, making it suitable for real-time applications.

In summary, convolution is a powerful mathematical operation that offers practical benefits in image processing by automatically extracting features, preserving spatial structure, learning patterns, and operating efficiently.


What is a gCNN?

A geodesic convolutional neural network (gCNN) uses geodesic convolutions instead of the grid-based 3D convolutions of a traditional 3D convolutional neural network, extending convolution to curved surfaces such as 3D meshes (Masci et al., 2015). Geodesic convolutions consider the intrinsic geometry of the processed data.

Instances are the curvature or shape of objects with bumps. gCNNs are suited to medical applications: for example, organs, bones, and tissues often have complex shapes that can be better captured and analyzed using geodesic convolutions. Separately, volumetric 3D CNNs are applied to CT and MRI scans for diagnostic purposes.

What are the advantages of gCNNs

The advantages are twofold:

  1. Geodesic convolutions can better analyze the data’s intrinsic geometry and improve the model accuracy.
  2. Geodesic convolutions can be more computationally efficient than traditional CNNs, as they only consider the most important information in the data. The reduced number of parameters in the model, the reduced number of computations required for each convolution operation, and the reduced amount of data to be processed all contribute to efficiency.

More on gCNNs

Traditional convolutional neural networks (CNNs) use a fixed grid structure to process input data, resulting in a loss of information about the data’s intrinsic geometry. On the other hand, geodesic convolutions use a flexible grid structure adapted to the data’s geometry, allowing a more accurate representation of the data’s intrinsic geometry. This is done by defining the grid structure in terms of geodesic distances, rather than Euclidean distances, between the data points. The geodesic distance between two points in the data can be computed using various techniques, including heat diffusion, shortest-path algorithms, or curvature-aware methods. The choice of technique will depend on the specific task and the type of data being processed.


What are Euclidean and non-Euclidean distances?

Euclidean and non-Euclidean distance measures are two types of distance measures used in CNNs.

  • Euclidean distance measures the straight-line distance between two points in space.
  • Non-Euclidean distance, on the other hand, refers to any distance measure that is not the Euclidean distance.

Euclidean distance

Euclidean distance is used in traditional convolutions.

In the context of CNNs, Euclidean distance defines the neighborhood covered by the filter in a traditional convolution operation. In this case, the filter is moved across the input in a grid-like pattern. At each position, the filter covers the grid points within fixed offsets. On a uniform grid, these offsets correspond to Euclidean distances.

Non-Euclidean distance

Non-Euclidean distance measures are used in geodesic convolutions to better capture the intrinsic geometry of the processed data.

In the context of CNNs, non-Euclidean distance measures can define the neighborhood covered by the filter in a geodesic convolution operation. In this case, the grid structure used to move the filter across the input is adapted to the data’s intrinsic geometry. The non-Euclidean distance measure, such as the geodesic distance along a surface, defines the extent of the filter’s neighborhood.

Cat example

A Euclidean manifold is a space with distance and coordinates.

In a 2D picture of a cat, pixels are points in the plane, with relationships captured by Euclidean distance, calculated as

√((x₂ – x₁)²+(y₂ – y₁)²)

Computing these distances between pixels helps in image segmentation, feature extraction, and clustering. Although pixel values are discrete, this simplified, continuous representation suffices for many image-processing tasks, enabling standard CNNs to process images effectively.

3D polygon mesh model of a cat

3D convolutional neural network applications

We can think of many applications for a 3D convolutional neural network, including:

  • Design space exploration
  • Industrial product design
  • Material Science
  • 3D CAD model

Design space exploration

One of the most impactful uses of 3D CNN-based prediction in engineering is not the evaluation of a single design, but the systematic exploration of large design spaces. When a fast predictive model is combined with parametric geometry generation, it becomes possible to evaluate thousands or millions of design configurations in a short time, identifying high-performing regions that would never have been discovered through manual iteration.

This capability is at the core of the Neural Concept platform. Through the Design Copilot, engineers can interact directly with the design space, steer exploration based on performance targets, and receive AI-assisted recommendations grounded in physics. Physics prediction models trained on 3D data are integrated with geometry generation, optimization pipelines, and human-in-the-loop interfaces into a single workflow. The result is not a simulation shortcut. It is a system that turns geometric and physical data into design decisions.

Industrial product design

In industrial product design, 3D CNNs are used to learn the mapping between CAD geometries and physical performance indicators such as drag, thermal distribution, stress concentrations, or acoustic behavior. Once trained on data generated from high-fidelity simulations, the model can predict those outputs for new geometries in a fraction of a second, enabling design engineers to evaluate hundreds of design variants without running a single additional simulation.

This approach is particularly valuable in competitive industries where development timelines are short, and the number of design options to explore is large. It removes the bottleneck between design and simulation teams, allowing performance feedback to be embedded directly into the design process rather than arriving at the end.

Material science

In materials science, 3D CNNs analyze volumetric imaging data such as X-ray computed tomography, electron microscopy stacks, and atomistic simulations. They learn spatial hierarchies of features from 3D structures, enabling tasks like defect detection, grain boundary segmentation, and phase classification. Input tensors represent 3D grayscale or multi-channel voxel data, and supervised training on annotated datasets means segmentation accuracy depends heavily on preprocessing quality. Error functions such as Dice loss or cross-entropy are used, and residual network components are common in deeper segmentation models. Models benefit from GPU-accelerated training due to high data dimensionality.

3D CAD models

Recognizing features in 3D CAD models is a critical step in automating design and manufacturing workflows, especially as traditional manufacturing transitions into smart factories.

Studying 3D CAD models is essential for the conversion of traditional manufacturing industries into smart factories. Conventional methods for recognizing machining features include graph-based, volume decomposition, hint-based, and similarity-based methods. However, the development of DL applications for machining feature recognition is motivated by the limitations of traditional methods.

FeatureNet utilizes a voxel dataset and 3D convolutional networks to recognize machining features in CAD models. Gradient-weighted class activation mapping (Grad-CAM) is used to identify salient regions in 3D CAD models using 3D CNNs.

3D CNNs have also been applied to human activity recognition, video classification, and medical image detection, demonstrating their versatility beyond CAD-specific applications.


Conclusions: 3D convolutional neural network applications – 3D simulation

3D Convolutional Neural Networks have established themselves as a foundational technology for applying deep learning to volumetric and geometric data. In engineering, their ability to learn spatial correlations between CAD geometry and physical behavior has opened the door to fast, data-driven predictions that were previously only accessible through costly and time-consuming numerical simulations.

The core shift they enable is structural. Rather than running each simulation independently, engineers can train a predictive model once on historical data and then use it to rapidly evaluate a large number of design variants. Predictions that would take hours using conventional CAE are delivered in seconds. This speed is not an end in itself, but the enabler of something more significant: the ability to explore design spaces that were previously out of reach.

For engineers entering the field of AI-driven product design, understanding 3D CNNs is an important step. It provides the conceptual foundation for how AI models learn from 3D data, why geometry representation matters, and what the real limits of data-driven prediction are.

This is also where Neural Concept started. Physics prediction from 3D geometry was the platform’s founding capability and remains a core part of it today, but it is one of several capabilities. Neural Concept has since grown into the intelligence layer for engineering that companies can own, tailor, and evolve internally, a platform that sits above the traditional CAD, CAE, and PLM stack. Physics prediction now sits alongside design space generation, simulation automation, AI copilots, and agentic workflows, all connected into a single environment where engineering teams can build, adapt, and scale their own AI-driven processes, rather than depend on a one-off surrogate model.

If you want to see how these capabilities work together in practice, explore the Neural Concept platform.


FAQ

What is the computational load when implementing 3D CNNs?

3D CNN implementations face computational challenges due to increased model complexity. 3D CNNs incur a significantly higher computational load than 2D CNNs because they process volumetric data with 3D kernels. This leads to increased memory usage, more parameters, and longer training times. Adding more dimensions increases data and model size exponentially. Training requires high-end GPUs or distributed systems, especially for large datasets such as videos or scans. Inference takes longer, limiting real-time deployment without hardware acceleration or optimization. Researchers are developing more efficient architectures and training techniques to address the challenges faced by 3D CNNs.

Why is it difficult to train 3D CNNs effectively?

3D CNNs often require large datasets for effective training, making data preparation a crucial step that can be difficult to obtain.

How much data is needed to train a 3D CNN for engineering prediction?

The most common misconception about training 3D CNNs for engineering prediction is that more data automatically means better results. In practice, data quality and the representativeness of the design space matter far more than volume. A dataset of a few hundred well-distributed simulation cases, covering the actual range of geometries and boundary conditions an engineering team will encounter, will consistently outperform a dataset of thousands of poorly sampled or redundant cases. What makes a dataset useful is whether it covers the design space the model will be asked to predict in. Gaps in coverage, inconsistent meshing, or data generated from a narrow set of boundary conditions will degrade prediction quality regardless of dataset size. In practice, industrial workflows at Neural Concept have been trained successfully on datasets ranging from a few dozen to several thousand simulation cases, with smaller, high-quality datasets frequently delivering production-ready results.

What is the difference between a 3D CNN and a physics simulation solver?

A physics simulation solver computes results from first principles, applying equations of fluid dynamics, structural mechanics, or thermodynamics to a given geometry and boundary conditions. A 3D CNN, by contrast, learns a statistical mapping between inputs and outputs from data. It does not solve equations; it approximates the relationship that a solver has already established through prior simulations. This makes it orders of magnitude faster at inference time, but its validity is limited to the training data distribution. Both approaches are complementary: the solver generates the data, and the 3D CNN operationalizes it at scale.

How does the training time of 3D CNNs compare to that of 2D CNNs?

The training time for 3D CNNs is significantly longer than for 2D CNNs due to their greater complexity.

What are the most common architectures used in 3D CNNs?

Popular 3D CNN architectures include C3D, which uses 3×3×3 kernels throughout; I3D, which inflates 2D filters into 3D from pretrained ImageNet models; and R(2+1)D, which factorizes 3D convolutions into separate spatial and temporal operations. These are widely used in video classification and action recognition pipelines.

How can we improve the generalization ability of 3D CNNs?

Regularization techniques are essential for improving the generalization of 3D CNNs. To improve the generalization of a 3D CNN, the idea is to make the model less dependent on quirks of the training data. During training, some connections can be randomly disabled so the network cannot rely on a single pathway and must learn more robust features. The weights can also be slightly penalized when they become too large, which discourages memorizing noise. In addition, varying the input data by changing orientation, scaling, or cropping of volumes forces the model to learn patterns that hold across different perspectives rather than memorizing fixed examples. Together, these techniques reduce overfitting and lead to better performance on unseen data.

How are 3D CNNs used in Neural Concept?

In the Neural Concept platform, 3D CNNs are used as the engine for physics prediction from 3D geometry. They are trained on simulation data to learn the relationship between CAD geometry and physical performance outputs such as drag, stress, thermal distribution, or acoustic behavior. Once trained, these models deliver predictions in a fraction of a second for any new geometry, enabling rapid evaluation across large design spaces. Within the platform, 3D CNN-based prediction models are not standalone tools. They are integrated into broader workflows that include parametric geometry generation, design space exploration, simulation automation, and AI copilot interfaces. The 3D CNN provides the physics intelligence; the platform connects it to the engineering process.

Is Neural Concept a surrogate modeling tool?

No. Neural Concept is the intelligence layer for engineering, a platform that helps engineering organizations accelerate and scale their product development processes using AI. Surrogate modeling, which involves training fast predictive models to replace computationally expensive simulations, is one of the platform's capabilities. It is not the platform itself. Beyond surrogate modeling, Neural Concept provides design space generation, simulation automation, AI co-pilots for engineers, and agentic workflows that connect geometry, physics, and enterprise systems. The platform is designed to be owned and adapted internally by engineering teams, encoding their specific know-how into scalable, reusable processes.

What is the difference between Neural Concept and traditional CAE software?

Traditional CAE software such as CFD or FEA solvers computes physical results from first principles for a single design configuration at a time. It is high-fidelity and highly accurate, but each evaluation is computationally expensive and time-consuming, typically taking hours to days per simulation run. Neural Concept does not replace CAE solvers. It sits above them. The platform uses simulation data generated by those solvers to train AI models that can then predict performance across thousands of design variants in seconds. This makes it possible to explore large design spaces, automate repetitive evaluation tasks, and embed physics intelligence into earlier stages of the design process, where traditional CAE is typically too slow to have an impact.

Can Neural Concept replace CFD or FEA simulations?

No, and this distinction matters. Neural Concept does not replace physics solvers. It is built on top of them. CFD and FEA solvers remain the source of ground truth: they compute results from first principles with high accuracy. Neural Concept uses the data generated by those solvers to train predictive models that can evaluate new design configurations in a fraction of the time. The value of this approach is not replacement but scale. A solver can evaluate one design at a time, often after expensive meshing of the 3D geometry. A trained model running on the Neural Concept platform can evaluate thousands of items. This makes it possible to explore design spaces, run optimization loops, and deliver physics feedback at stages of the design process where running a full simulation would be too slow or too expensive.

Can a 3D CNN predict any type of physics?

In principle, a 3D CNN can learn any mapping between a geometric input and a physical output, provided that sufficient training data exists and the underlying relationship is learnable from that data. In practice, the model's accuracy and reliability depend heavily on how well the training data covers the geometry variations and physical conditions the model will encounter at inference time. Aerodynamic performance, structural stress, thermal distribution, and acoustic behavior are among the physical phenomena that have been successfully predicted using 3D CNN-based models in industrial environments. More complex, highly non-linear phenomena with strong sensitivity to boundary conditions require more data and more careful design of the training pipeline. At Neural Concept, the platform is designed to support the building, validation, and deployment of models within engineering workflows.

What is an engineering intelligence layer?

An engineering intelligence layer is a software layer that sits above the existing CAD, CAE, and PLM stack and connects AI capabilities directly to engineering workflows. Rather than replacing existing tools, it integrates with them to add capabilities they do not natively provide: fast physics prediction from 3D geometry, parametric design space generation, simulation automation, and AI-assisted decision support. The concept is relevant to 3D CNN-based systems because those models do not operate in isolation. A 3D CNN that predicts drag from a CAD geometry is only useful if it is connected to a geometry pipeline, a design evaluation interface, and a way for engineers to act on its outputs. The intelligence layer is what makes that connection possible. Neural Concept is built on this principle: the platform provides the infrastructure to turn individual AI models, including 3D CNN-based physics predictors, into integrated engineering workflows.