# A non-cooperative meta-modeling game for automated third-party calibrating, validating, and falsifying constitutive laws with parallelized adversarial attacks

arXiv: https://arxiv.org/abs/2004.09392 · HTML: https://mlsanity.com/paper/2004.09392/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Apr 2020.

## Built on by (most cited first, 8 of 8)

- [A review on data-driven constitutive laws for solids](https://mlsanity.com/paper/2405.03658/) (2024)
- [Equivariant geometric learning for digital rock physics: estimating formation factor and effective permeability tensors from Morse graph](https://mlsanity.com/paper/2104.05608/) (2021)
- [Geometric deep learning for computational mechanics Part II: Graph embedding for interpretable multiscale plasticity](https://mlsanity.com/paper/2208.00246/) (2022)
- [Physics-Informed Deep Learning For Traffic State Estimation: A Survey and the Outlook](https://mlsanity.com/paper/2303.02063/) (2023)
- [Data-driven discovery of interpretable causal relations for deep learning material laws with uncertainty propagation](https://mlsanity.com/paper/2105.09980/) (2021)
- [Discovering interpretable elastoplasticity models via the neural polynomial method enabled symbolic regressions](https://mlsanity.com/paper/2307.13149/) (2023)
- [Design of experiments for the calibration of history-dependent models via deep reinforcement learning and an enhanced Kalman filter](https://mlsanity.com/paper/2209.13126/) (2022)
- [Towards scientific machine learning for granular material simulations -- challenges and opportunities](https://mlsanity.com/paper/2504.08766/) (2025)

## Abstract (arXiv)

The evaluation of constitutive models, especially for high-risk and high-regret engineering applications, requires efficient and rigorous third-party calibration, validation and falsification. While there are numerous efforts to develop paradigms and standard procedures to validate models, difficulties may arise due to the sequential, manual and often biased nature of the commonly adopted calibration and validation processes, thus slowing down data collections, hampering the progress towards discovering new physics, increasing expenses and possibly leading to misinterpretations of the credibility and application ranges of proposed models. This work attempts to introduce concepts from game theory and machine learning techniques to overcome many of these existing difficulties. We introduce an automated meta-modeling game where two competing AI agents systematically generate experimental data to calibrate a given constitutive model and to explore its weakness, in order to improve experiment design and model robustness through competition. The two agents automatically search for the Nash equilibrium of the meta-modeling game in an adversarial reinforcement learning framework without human intervention. By capturing all possible design options of the laboratory experiments into a single decision tree, we recast the design of experiments as a game of combinatorial moves that can be resolved through deep reinforcement learning by the two competing players. Our adversarial framework emulates idealized scientific collaborations and competitions among researchers to achieve a better understanding of the application range of the learned material laws and prevent misinterpretations caused by conventional AI-based third-party validation.