# HYCO: A Formalism for Hybrid-Cooperative PDE Modelling

arXiv: https://arxiv.org/abs/2602.23859 · HTML: https://mlsanity.com/paper/2602.23859/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2026.

## Built on by (most cited first, 1 of 1)

- [Bi-HYCO: Bi-Objective Cooperative Learning for PDE Parameter Identification under Fragmented Observations](https://mlsanity.com/paper/2609.06511/) (2026)

## Abstract (arXiv)

We present Hybrid-Cooperative Learning (HYCO), a hybrid modeling framework that integrates physics-based and data-driven models through mutual regularization. Unlike traditional approaches that impose physical constraints directly on synthetic models, HYCO treats both components as co-trained agents nudged toward agreement. This cooperative scheme is naturally parallelizable and demonstrates robustness to sparse and noisy data. Numerical experiments on static and time-dependent benchmark problems show that HYCO can recover accurate solutions and model parameters under ill-posed conditions. The framework admits a game-theoretic interpretation as a Nash equilibrium problem, enabling alternating optimization. This paper is based on the extended preprint: arXiv:2509.14123 .