# Evaluating Dynamical Fidelity through Predictive Structure in Physical Representations

arXiv: https://arxiv.org/abs/2609.34627 · HTML: https://mlsanity.com/paper/2609.34627/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 39 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 18 of 18)

- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [WeatherBench 2: A benchmark for the next generation of data-driven global weather models](https://mlsanity.com/paper/2308.15560/) (2023)
- [FengWu: Pushing the Skillful Global Medium-range Weather Forecast beyond 10 Days Lead](https://mlsanity.com/paper/2304.02948/) (2023)
- [Machine learning for molecular simulation](https://mlsanity.com/paper/1911.02792/) (2019)
- [Learning Physical Models that Can Respect Conservation Laws](https://mlsanity.com/paper/2302.11002/) (2023)
- [Can AI weather models predict out-of-distribution gray swan tropical cyclones?](https://mlsanity.com/paper/2410.14932/) (2024)
- [Dynamical Tests of a Deep-Learning Weather Prediction Model](https://mlsanity.com/paper/2309.10867/) (2023)
- [Harnessing the Power of Neural Operators with Automatically Encoded Conservation Laws](https://mlsanity.com/paper/2312.11176/) (2023)
- [PhysMetrics.Weather: An Evaluation Framework for Physical Consistency in ML Weather Models](https://mlsanity.com/paper/2606.10642/) (2026)
- [A Numerical Proof of Shell Model Turbulence Closure](https://mlsanity.com/paper/2202.09289/) (2022)
- [Evaluating the Transferability of Machine-Learned Force Fields for Material Property Modeling](https://mlsanity.com/paper/2301.03729/) (2023)
- [Investigating Inductive Biases for Machine Learning Emulation of Sudden Stratospheric Warmings in Idealised Isca Simulations](https://mlsanity.com/paper/2606.18857/) (2026)

## Abstract (arXiv)

Machine-learning models for physical systems are currently evaluated primarily through errors between predicted and reference states and, increasingly, through tests of physical consistency. These metrics assess whether predictions are accurate and satisfy selected physical requirements, but provide limited insight into whether learned trajectories reproduce the underlying dynamics. Domain experts examine such relationships through physical representations that expose relevant processes, interactions, and responses, but these analyses are often separated from typical machine-learning evaluation. We introduce a practical framework for evaluating dynamical fidelity through predictive structure in physical representation spaces. Experts define the representations, while reference trajectories determine which relationships are predictive and retained as evaluation tests. We demonstrate the approach in atmospheric forecasting using ERA5 representations of planetary-wave activity and Northern Annular Mode evolution, and evaluate Pangu-Weather, GraphCast, and FengWu. The models exhibit distinct departures from reference predictive structure that are not reflected by conventional forecast errors. The framework thereby turns domain-expert representations into systematic tests of learned physical dynamics without prescribing the relationships in advance.