# Verification and Validation for Trustworthy Scientific Machine Learning

arXiv: https://arxiv.org/abs/2502.15496 · HTML: https://mlsanity.com/paper/2502.15496/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 133 references that are in the map.
- First posted on arXiv 21 Feb 2025.

## Builds on (most cited first, 30 of 44)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [The Mythos of Model Interpretability](https://mlsanity.com/paper/1606.03490/) (2016)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [Model Reduction and Neural Networks for Parametric PDEs](https://mlsanity.com/paper/2005.03180/) (2020)
- [Machine Learning Testing: Survey, Landscapes and Horizons](https://mlsanity.com/paper/1906.10742/) (2019)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Formalizing Trust in Artificial Intelligence: Prerequisites, Causes and Goals of Human Trust in AI](https://mlsanity.com/paper/2010.07487/) (2020)
- [Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behavior](https://mlsanity.com/paper/2306.00258/) (2023)
- [Interpretable Machine Learning -- A Brief History, State-of-the-Art and Challenges](https://mlsanity.com/paper/2010.09337/) (2020)
- [Physics-Informed Deep Neural Operator Networks](https://mlsanity.com/paper/2207.05748/) (2022)
- [Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations](https://mlsanity.com/paper/2407.07218/) (2024)
- [POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition](https://mlsanity.com/paper/2101.11845/) (2021)
- [The relationship between trust in AI and trustworthy machine learning technologies](https://mlsanity.com/paper/1912.00782/) (2019)
- [Rates of Convergence for Sparse Variational Gaussian Process Regression](https://mlsanity.com/paper/1903.03571/) (2019)
- [Deep Gaussian Processes for Multi-fidelity Modeling](https://mlsanity.com/paper/1903.07320/) (2019)
- [Derivative-Informed Neural Operator: An Efficient Framework for High-Dimensional Parametric Derivative Learning](https://mlsanity.com/paper/2206.10745/) (2022)
- [Conditional Sampling with Monotone GANs: from Generative Models to Likelihood-Free Inference](https://mlsanity.com/paper/2006.06755/) (2020)
- [On the representation and learning of monotone triangular transport maps](https://mlsanity.com/paper/2009.10303/) (2020)
- [Adoption and Effects of Software Engineering Best Practices in Machine Learning](https://mlsanity.com/paper/2007.14130/) (2020)
- [Fast PDE-constrained optimization via self-supervised operator learning](https://mlsanity.com/paper/2110.13297/) (2021)
- [Neural and spectral operator surrogates: unified construction and expression rate bounds](https://mlsanity.com/paper/2207.04950/) (2022)
- [Machine Learning-augmented Predictive Modeling of Turbulent Separated Flows over Airfoils](https://mlsanity.com/paper/1608.03990/) (2016)
- [Deep Learning of Preconditioners for Conjugate Gradient Solvers in Urban Water Related Problems](https://mlsanity.com/paper/1906.06925/) (2019)

## Built on by (most cited first, 4 of 4)

- [HyCOP: Hybrid Composition Operators for Interpretable Learning of PDEs](https://mlsanity.com/paper/2605.00820/) (2026)
- [Energy-efficient operation of neural operators for virtual sensing](https://mlsanity.com/paper/2609.30580/) (2026)
- [Enabling Real-Time Training of a Wildfire-to-Smoke Map with Multilinear Operators](https://mlsanity.com/paper/2605.04164/) (2026)
- [A Continual Validation, Updating, and Decision-Making Framework for Self-Adaptive Digital Twins via Robust Model Predictive Control: A Case Study in Additive Manufacturing](https://mlsanity.com/paper/2607.18164/) (2026)

## Abstract (arXiv)

Scientific machine learning (SciML) models are transforming many scientific disciplines. However, the development of good modeling practices to increase the trustworthiness of SciML has lagged behind its application, limiting its potential impact. The goal of this paper is to start a discussion on establishing consensus-based good practices for predictive SciML. We identify key challenges in applying existing computational science and engineering guidelines, such as verification and validation protocols, and provide recommendations to address these challenges. Our discussion focuses on predictive SciML, which uses machine learning models to learn, improve, and accelerate numerical simulations of physical systems. While centered on predictive applications, our 16 recommendations aim to help researchers conduct and document their modeling processes rigorously across all SciML domains.