Scientific machine learning

Key works

Neural optimization

Neural optimization reparametrizes the design variables, such as the pixels in topology optimization, with a neural network. Instead of optimizing the design variables directly, the network predicts them, and its weights are optimized.

In structural optimization, this finds better optima.

Standard optimization

Neural reparametrization

In inverse problems, it yields regularized solutions.

Measurement

Standard

Neural

And with prior knowledge through transfer learning, optimizations become faster.

Standard

Neural

Pretrained

Anomaly detection

Generative models can serve as anomaly detectors: a structure that the model cannot generate is flagged as an anomaly.

Normal data

Input

Reconstruction

Error

Anomalous data

Methodological overview

Neural networks can represent almost anything efficiently.

Getting them to do so is challenging, though, particularly in mechanics. Our methodological review gives an overview. To learn about these methods, we provide our textbook, in its first and second edition, and the neuralmech platform, with an accompanying book draft that is available on request.

deep-learning-in-computational-mechanics

Code for the textbook.

neuralmech

Machine learning enhanced solvers and optimizers.

Publications

• Graph neural networks for full waveform inversion Computational Mechanics, 2026

  Learns on the mesh graph to invert wave measurements for unknown material fields.

  Code
• Lightweight return-mapping surrogates for multiscale plasticity: a practical guide Computational Mechanics, 2026

  Replaces the return-mapping step of plasticity with small, reliable learned surrogates.

  Code
• Accelerating full waveform inversion by transfer learning Computational Mechanics, 2025

  Reuses networks trained on earlier reconstructions to shorten new inversions.

  Code
• Deep learning in computational mechanics: a review Computational Mechanics, 2024

  A methodological survey of where deep learning has, and has not, proven useful in mechanics.

• On neural networks for generating better local optima in topology optimization Structural and Multidisciplinary Optimization, 2024

  Uses a neural reparametrization of the design field to escape poor local optima.

  Code
• Generative adversarial networks enable outlier detection and property monitoring for additive manufacturing of complex structures Engineering Applications of Artificial Intelligence, 2024

  Flags anomalous prints and tracks properties from process data using a GAN.

  Data
• On the use of neural networks for full waveform inversion Computer Methods in Applied Mechanics and Engineering, 2023

  Discovers neural reparametrizations for regularization in inverse problems.

• Quantitative reconstruction of defects in multi-layered bonded composites using fully convolutional network-based ultrasonic inversion Journal of Sound and Vibration, 2023

  Reconstructs defects in bonded multi-layer composites from ultrasonic signals with a fully convolutional network.