# Optimal Experimental Design for Reliable Learning of History-Dependent Constitutive Laws arXiv: https://arxiv.org/abs/2603.12365 · HTML: https://mlsanity.com/paper/2603.12365/ ## Key facts - Cited by 1 papers in the map (data through 14 Oct 2026). - Builds on 27 of its 111 references that are in the map. - First posted on arXiv 12 Mar 2026. ## Builds on (most cited first, 27 of 27) - [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019) - [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023) - [Variational Bayesian Optimal Experimental Design](https://mlsanity.com/paper/1903.05480/) (2019) - [On Nesting Monte Carlo Estimators](https://mlsanity.com/paper/1709.06181/) (2017) - [Optimal experimental design: Formulations and computations](https://mlsanity.com/paper/2407.16212/) (2024) - [Derivative-Informed Neural Operator: An Efficient Framework for High-Dimensional Parametric Derivative Learning](https://mlsanity.com/paper/2206.10745/) (2022) - [A review on data-driven constitutive laws for solids](https://mlsanity.com/paper/2405.03658/) (2024) - [Sequential Bayesian optimal experimental design via approximate dynamic programming](https://mlsanity.com/paper/1604.08320/) (2016) - [Large-scale Bayesian optimal experimental design with derivative-informed projected neural network](https://mlsanity.com/paper/2201.07925/) (2022) - [Multilevel Monte Carlo estimation of expected information gains](https://mlsanity.com/paper/1811.07546/) (2018) - [Derivative-informed neural operator acceleration of geometric MCMC for infinite-dimensional Bayesian inverse problems](https://mlsanity.com/paper/2403.08220/) (2024) - [Variational Bayesian Optimal Experimental Design with Normalizing Flows](https://mlsanity.com/paper/2404.13056/) (2024) - [Bayesian model calibration for block copolymer self-assembly: Likelihood-free inference and expected information gain computation via measure transport](https://mlsanity.com/paper/2206.11343/) (2022) - [Accurate, scalable, and efficient Bayesian optimal experimental design with derivative-informed neural operators](https://mlsanity.com/paper/2312.14810/) (2023) - [A fast and scalable computational framework for large-scale and high-dimensional Bayesian optimal experimental design](https://mlsanity.com/paper/2010.15196/) (2020) - [A-optimal design of experiments for infinite-dimensional Bayesian linear inverse problems with regularized ℓ0-sparsification](https://mlsanity.com/paper/1308.4084/) (2013) - [hIPPYlib: An Extensible Software Framework for Large-Scale Inverse Problems Governed by PDEs; Part I: Deterministic Inversion and Linearized Bayesian Inference](https://mlsanity.com/paper/1909.03948/) (2019) - [Tractable Optimal Experimental Design using Transport Maps](https://mlsanity.com/paper/2401.07971/) (2024) - [LazyDINO: Fast, scalable, and efficiently amortized Bayesian inversion via structure-exploiting and surrogate-driven measure transport](https://mlsanity.com/paper/2411.12726/) (2024) - [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) - [A topology optimisation framework to design test specimens for one-shot identification or discovery of material models](https://mlsanity.com/paper/2501.12756/) (2025) - [Learning Memory and Material Dependent Constitutive Laws](https://mlsanity.com/paper/2502.05463/) (2025) - [Inference of Heterogeneous Material Properties via Infinite-Dimensional Integrated DIC](https://mlsanity.com/paper/2408.10217/) (2024) - [Expected information gain estimation via density approximations: Sample allocation and dimension reduction](https://mlsanity.com/paper/2411.08390/) (2024) - [An approach for finding fully Bayesian optimal designs using normal-based approximations to loss functions](https://mlsanity.com/paper/1608.05815/) (2016) - [Bayesian Optimal Experimental Design for Constitutive Model Calibration](https://mlsanity.com/paper/2308.10702/) (2023) - [Mechanics Informatics: A paradigm for efficiently learning constitutive models](https://mlsanity.com/paper/2501.08314/) (2025) ## Built on by (most cited first, 1 of 1) - [HPG-Diff: Hierarchical physics-guided diffusion with differentiable connectivity constraints for topology optimization](https://mlsanity.com/paper/2607.07233/) (2026) ## Abstract (arXiv) History-dependent constitutive models serve as macroscopic closures for the aggregated effects of micromechanics. Their parameters are typically learned from experimental data. With a limited experimental budget, eliciting the full range of responses needed to characterize the constitutive relation can be difficult. As a result, the data can be well explained by a range of parameter choices, leading to parameter estimates that are uncertain or unreliable. To address this issue, we propose a Bayesian optimal experimental design framework to quantify, interpret, and maximize the utility of experimental designs for reliable learning of history-dependent constitutive models. In this framework, the design utility is defined as the expected reduction in parametric uncertainty or the expected information gain. This enables in silico design optimization using simulated data and reduces the cost of physical experiments for reliable parameter identification. We introduce two approximations that make this framework practical for advanced material testing with expensive forward models and high-dimensional data: (i) a Gaussian approximation of the expected information gain, and (ii) a surrogate approximation of the Fisher information matrix. The former enables efficient design optimization and interpretation, while the latter extends this approach to batched design optimization by amortizing the cost of repeated utility evaluations. Our numerical studies of uniaxial tests for viscoelastic solids show that optimized specimen geometries and loading paths yield image and force data that significantly improve parameter identifiability relative to random designs, especially for parameters associated with memory effects.