# Environment Inference for Learning Generalizable Dynamical System

arXiv: https://arxiv.org/abs/2510.19784 · HTML: https://mlsanity.com/paper/2510.19784/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 45 references that are in the map.
- First posted on arXiv 22 Oct 2025.

## Builds on (most cited first, 23 of 23)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Deep Domain Confusion: Maximizing for Domain Invariance](https://mlsanity.com/paper/1412.3474/) (2014)
- [Generalizing to Unseen Domains via Adversarial Data Augmentation](https://mlsanity.com/paper/1805.12018/) (2018)
- [Domain Generalization by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1903.06864/) (2019)
- [Unified Deep Supervised Domain Adaptation and Generalization](https://mlsanity.com/paper/1709.10190/) (2017)
- [Generalizing Across Domains via Cross-Gradient Training](https://mlsanity.com/paper/1804.10745/) (2018)
- [Fairness without Demographics through Adversarially Reweighted Learning](https://mlsanity.com/paper/2006.13114/) (2020)
- [Episodic Training for Domain Generalization](https://mlsanity.com/paper/1902.00113/) (2019)
- [Learning to Optimize Domain Specific Normalization for Domain Generalization](https://mlsanity.com/paper/1907.04275/) (2019)
- [Efficient Domain Generalization via Common-Specific Low-Rank Decomposition](https://mlsanity.com/paper/2003.12815/) (2020)
- [Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge](https://mlsanity.com/paper/1711.07970/) (2017)
- [Domain Generalization via Multidomain Discriminant Analysis](https://mlsanity.com/paper/1907.11216/) (2019)
- [Robustness to Spurious Correlations via Human Annotations](https://mlsanity.com/paper/2007.06661/) (2020)
- [Generalizing to New Physical Systems via Context-Informed Dynamics Model](https://mlsanity.com/paper/2202.01889/) (2022)
- [LEADS: Learning Dynamical Systems that Generalize Across Environments](https://mlsanity.com/paper/2106.04546/) (2021)
- [Meta-Learning Dynamics Forecasting Using Task Inference](https://mlsanity.com/paper/2102.10271/) (2021)
- [Out-of-Domain Generalization in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2402.18377/) (2024)
- [Data-driven approaches for predicting spread of infectious diseases through DINNs: Disease Informed Neural Networks](https://mlsanity.com/paper/2110.05445/) (2021)

## Built on by (most cited first, 2 of 2)

- [RoME: Domain-Robust Mixture-of-Experts for MILP Solution Prediction across Domains](https://mlsanity.com/paper/2511.02331/) (2025)
- [Beyond Rational Illusion: Behaviorally Realistic Strategic Classification](https://mlsanity.com/paper/2605.19674/) (2026)

## Abstract (arXiv)

Data-driven methods offer efficient and robust solutions for analyzing complex dynamical systems but rely on the assumption of I.I.D. data, driving the development of generalization techniques for handling environmental differences. These techniques, however, are limited by their dependence on environment labels, which are often unavailable during training due to data acquisition challenges, privacy concerns, and environmental variability, particularly in large public datasets and privacy-sensitive domains. In response, we propose DynaInfer, a novel method that infers environment specifications by analyzing prediction errors from fixed neural networks within each training round, enabling environment assignments directly from data. We prove our algorithm effectively solves the alternating optimization problem in unlabeled scenarios and validate it through extensive experiments across diverse dynamical systems. Results show that DynaInfer outperforms existing environment assignment techniques, converges rapidly to true labels, and even achieves superior performance when environment labels are available.