# Physics-conforming Latent Twins

arXiv: https://arxiv.org/abs/2606.15053 · HTML: https://mlsanity.com/paper/2606.15053/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 47 references that are in the map.
- First posted on arXiv 13 Jun 2026.

## Builds on (most cited first, 20 of 20)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics](https://mlsanity.com/paper/2004.02322/) (2020)
- [Operator Learning with Neural Fields: Tackling PDEs on General Geometries](https://mlsanity.com/paper/2306.07266/) (2023)
- [Continuous PDE Dynamics Forecasting with Implicit Neural Representations](https://mlsanity.com/paper/2209.14855/) (2022)
- [CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representations](https://mlsanity.com/paper/2206.02607/) (2022)
- [Machine learning structure preserving brackets for forecasting irreversible processes](https://mlsanity.com/paper/2106.12619/) (2021)
- [gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification](https://mlsanity.com/paper/2204.12005/) (2022)
- [tLaSDI: Thermodynamics-informed latent space dynamics identification](https://mlsanity.com/paper/2403.05848/) (2024)
- [Weak-Form Latent Space Dynamics Identification](https://mlsanity.com/paper/2311.12880/) (2023)
- [GoRINNs: Godunov-Riemann Informed Neural Networks for Learning Hyperbolic Conservation Laws](https://mlsanity.com/paper/2410.22193/) (2024)
- [Thermodynamically Consistent Latent Dynamics Identification for Parametric Systems](https://mlsanity.com/paper/2506.08475/) (2025)
- [Sparse L1-Autoencoders for Scientific Data Compression](https://mlsanity.com/paper/2405.14270/) (2024)
- [Guaranteeing Conservation Laws with Projection in Physics-Informed Neural Networks](https://mlsanity.com/paper/2410.17445/) (2024)
- [Latent Twins](https://mlsanity.com/paper/2509.20615/) (2025)
- [Next Generation Equation-Free Multiscale Modelling of Crowd Dynamics via Machine Learning](https://mlsanity.com/paper/2508.03926/) (2025)

## Abstract (arXiv)

Surrogate models are central to scientific machine learning, where they enable fast prediction, simulation, inference, and control for complex physical systems. For time-dependent problems, however, accurate interpolation of training trajectories is not sufficient: reliable surrogates should also respect the conservation laws, invariants, admissibility conditions, and dissipative structures that give those trajectories physical meaning. We introduce Physics-conforming Latent Twins, a framework for learning latent surrogate solution operators whose dynamics satisfy selected physical principles by design. The method builds on the Latent Twin formulation by jointly learning an encoder, a decoder, and a latent flow map between arbitrary time-indexed states, while constraining the latent dynamics to preserve or dissipate prescribed structural quantities. We develop a constraint-transfer viewpoint that connects physical structure in the original state space with compatible constraints in latent space, and prove structure-preservation bounds showing how latent enforcement improves control of physical defects after decoding. We also derive algebraic conditions for latent flow maps that preserve linear and quadratic invariants or enforce dissipative inequalities. Numerical experiments on representative ODE and PDE benchmarks demonstrate improved constraint satisfaction, structural fidelity, and qualitative long-time behavior while maintaining accurate surrogate prediction.