Martin Vild

Výuka na FAST, VUT

BOA002 - Prvky kovových konstrukcí

BOA008 - Kovové konstrukce I

BOA001 - Konstrukce a dopravní stavby (část KDK)

BOA009 - Kovové konstrukce II

BO02 - Prvky kovových konstrukcí

Další prezentace

Short introduction to machine learning for science and engineering.

Machine Learning

This course introduces machine learning as a powerful tool for modelling complex, nonlinear relationships in data. Students will learn the fundamentals of neural networks, model training, and inference, with a focus on applications in science and engineering. Emphasis is placed on practical implementation and on the role of ML in complementing traditional computational methods.

Core terminology

Machine learning (ML): Methods that learn patterns from data to make predictions or decisions.
Dataset: Collection of input-output examples used for training and evaluation.
Feature / label: Input variables and corresponding outputs, also called targets.
Model: Mathematical representation that maps inputs to outputs.
Training / inference: Training fits the model to data; inference applies it to new data.
Supervised / unsupervised learning: Learning from labelled data, or discovering structure without labels.
Neural network: Layered model of interconnected neurons approximating complex functions.
Loss function / optimization: Prediction error and the process used to minimize it.
Validation / test set: Data used to assess performance during and after training.
Regularization / uncertainty: Tools for improving robustness and quantifying confidence in predictions.

Motivation

Machine learning is able to predict highly nonlinear relationships with remarkable accuracy in an automated manner. The approximation of complex input–output mappings by models such as neural networks enables the capture of interactions that are difficult or impractical to describe using traditional analytical formulations. This capability is particularly valuable in science and engineering, where governing relationships are often implicit, high-dimensional, or computationally expensive to evaluate. By learning directly from data, machine learning can significantly accelerate prediction, support parametric studies, and complement established numerical methods, thereby enabling more efficient and informed decision-making. In addition, trained models can be used as fast surrogate models to generate large volumes of synthetic data for Monte Carlo simulations, enabling direct reliability assessment with substantially reduced computational cost compared to conventional high-fidelity numerical analyses.

Figure 1: Deep neural network (DNN) prediction of numerical models of column web in transverse compression component (source https://doi.org/10.5281/zenodo.18017716)

Deep neural networks

Deep neural networks (DNNs) are a class of machine learning models composed of multiple interconnected layers of artificial neurons, enabling the hierarchical extraction of features from input data. Each layer applies a linear transformation followed by a nonlinear activation function, allowing the network to approximate highly complex and nonlinear relationships. By stacking many layers, DNNs can progressively learn low-level to high-level representations, which makes them particularly powerful for tasks involving high-dimensional data and intricate dependencies. Training is typically performed using backpropagation combined with gradient-based optimization, where model parameters are iteratively updated to minimize a defined loss function. Due to their flexibility and expressive capacity, DNNs are widely used in scientific computing and engineering as surrogate models, capturing complex physical behaviour with high accuracy while maintaining fast inference.

How training works

In a typical supervised learning workflow, the available dataset is first divided into training, validation, and test subsets. The training set is used to update the network parameters, the validation set helps monitor generalization and tune hyperparameters, and the test set is reserved for the final unbiased performance assessment. During each training iteration, input data are passed forward through the network, where each layer applies weighted sums and nonlinear activation functions such as ReLU, sigmoid, or tanh to build increasingly expressive representations. The prediction error is measured by a loss function, and backpropagation computes gradients of this loss with respect to the model parameters. An optimizer such as stochastic gradient descent or Adam then updates the weights step by step to reduce the error over many epochs, ideally leading to a model that performs well not only on the training data but also on previously unseen examples.

Limitations and engineering considerations

Despite their strong predictive capability, machine learning models—particularly deep neural networks—have important limitations that must be carefully considered in engineering applications. A key issue is their limited ability to extrapolate: predictions outside the range of the training data can be highly unreliable, even if the model performs well within the training domain. Unlike physics-based models, ML models do not inherently respect governing laws unless explicitly enforced, which may lead to non-physical or unsafe predictions. Engineers should therefore ensure that input data remain within the validated domain, monitor feature ranges, and apply appropriate safeguards such as input validation, conservative bounds, or hybrid modelling approaches. In critical applications, uncertainty quantification and verification against experiments or high-fidelity simulations remain essential.

Practical relevance and outlook

In practice, machine learning is already used across engineering domains: as surrogate models replacing computationally expensive finite element analyses, for rapid design space exploration, for real-time structural health monitoring, for inverse identification of material parameters, and for reliability assessment via Monte Carlo simulations with learned response functions. These applications show that ML is not a replacement for engineering knowledge, but a powerful extension of it. Understanding both its capabilities and limitations opens the door to a new class of data-driven design methodologies.

Selected resources

Google Machine Learning Crash Course – introductory explanations, examples, and figures.
ETH Zürich CAMLab – Machine Learning for Science and Engineering – engineering-oriented overview and visual material.
ETH Zürich – AI in the Sciences and Engineering – course page with clean neural-network figures.
Podcast source – general inspiration and broader context.

BOA002 - Prvky kovových konstrukcí

BOA008 - Kovové konstrukce I

BOA001 - Konstrukce a dopravní stavby (část KDK)

BOA009 - Kovové konstrukce II

BO02 - Prvky kovových konstrukcí

Další prezentace

Užitečné odkazy:

Zajímavé podcasty:

Normy:

Výukové licence:

Machine Learning

Core terminology

Motivation

Deep neural networks

How training works

Limitations and engineering considerations

Practical relevance and outlook

Selected resources

Structural Engineering

Roles in the Construction Industry

Evolution of Structures

Materials Used in Construction

External Forces and Boundary Conditions

Internal Forces

Limit State Design

Cross-Section

What is Good Design?

Steel Structures – Focused on Connections

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