# Machine Learning in Heterogeneous Porous Materials

arXiv: https://arxiv.org/abs/2202.04137 · HTML: https://mlsanity.com/paper/2202.04137/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 192 references that are in the map.
- First posted on arXiv 4 Feb 2022.

## Builds on (most cited first, 30 of 49)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [AutoML: A Survey of the State-of-the-Art](https://mlsanity.com/paper/1908.00709/) (2019)
- [AMC: AutoML for Model Compression and Acceleration on Mobile Devices](https://mlsanity.com/paper/1802.03494/) (2018)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [Deep Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/1804.04272/) (2018)
- [Weak SINDy For Partial Differential Equations](https://mlsanity.com/paper/2007.02848/) (2020)
- [PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison](https://mlsanity.com/paper/1703.00512/) (2017)
- [SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics](https://mlsanity.com/paper/2004.02322/) (2020)
- [An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications](https://mlsanity.com/paper/1908.10407/) (2019)
- [Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't](https://mlsanity.com/paper/2009.10713/) (2020)
- [An Open Source AutoML Benchmark](https://mlsanity.com/paper/1907.00909/) (2019)
- [A Differentiable Programming System to Bridge Machine Learning and Scientific Computing](https://mlsanity.com/paper/1907.07587/) (2019)
- [A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder](https://mlsanity.com/paper/2009.11990/) (2020)
- [Sparse learning of stochastic dynamic equations](https://mlsanity.com/paper/1712.02432/) (2017)
- [A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems](https://mlsanity.com/paper/1908.05823/) (2019)
- [Meta-learning PINN loss functions](https://mlsanity.com/paper/2107.05544/) (2021)
- [Learning Functional Priors and Posteriors from Data and Physics](https://mlsanity.com/paper/2106.05863/) (2021)
- [A Phase Shift Deep Neural Network for High Frequency Approximation and Wave Problems](https://mlsanity.com/paper/1909.11759/) (2019)
- [A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks](https://mlsanity.com/paper/2105.13136/) (2021)
- [SINDy-BVP: Sparse Identification of Nonlinear Dynamics for Boundary Value Problems](https://mlsanity.com/paper/2005.10756/) (2020)
- [Machine learning materials physics: Multi-resolution neural networks learn the free energy and nonlinear elastic response of evolving microstructures](https://mlsanity.com/paper/2001.01575/) (2019)
- [Efficient nonlinear manifold reduced order model](https://mlsanity.com/paper/2011.07727/) (2020)
- [A data-driven peridynamic continuum model for upscaling molecular dynamics](https://mlsanity.com/paper/2108.04883/) (2021)

## Built on by (most cited first, 3 of 3)

- [Partial Differential Equations Meet Deep Neural Networks: A Survey](https://mlsanity.com/paper/2211.05567/) (2022)
- [AI-driven inverse design of materials: Past, present and future](https://mlsanity.com/paper/2411.09429/) (2024)
- [Auto-weighted Bayesian Physics-Informed Neural Networks and robust estimations for multitask inverse problems in pore-scale imaging of dissolution](https://mlsanity.com/paper/2308.12864/) (2023)

## Abstract (arXiv)

The "Workshop on Machine learning in heterogeneous porous materials" brought together international scientific communities of applied mathematics, porous media, and material sciences with experts in the areas of heterogeneous materials, machine learning (ML) and applied mathematics to identify how ML can advance materials research. Within the scope of ML and materials research, the goal of the workshop was to discuss the state-of-the-art in each community, promote crosstalk and accelerate multi-disciplinary collaborative research, and identify challenges and opportunities. As the end result, four topic areas were identified: ML in predicting materials properties, and discovery and design of novel materials, ML in porous and fractured media and time-dependent phenomena, Multi-scale modeling in heterogeneous porous materials via ML, and Discovery of materials constitutive laws and new governing equations. This workshop was part of the AmeriMech Symposium series sponsored by the National Academies of Sciences, Engineering and Medicine and the U.S. National Committee on Theoretical and Applied Mechanics.