Bi-HYCO: Bi-Objective Cooperative Learning for PDE Parameter Identification under Fragmented Observations
Abstract
Physical and synthetic models may describe complementary aspects of the same PDE-governed system while receiving different, possibly fragmented, observations. We propose Bi-Objective HYCO (Bi-HYCO), a cooperative framework that retains both representations and their local observational objectives while coupling their predicted states at unlabeled interaction points. These points contain no measurements and do not augment the data; they provide a communication mechanism in the common state space. The two criteria form a vector-valued objective, and weighted scalarizations provide computational realizations. For the deterministic shared-observation algorithm with fixed interaction points, we prove sufficient decrease and finite length of the whole alternating sequence, which converges to a mixed critical point under the stated Kurdyka-Lojasiewicz-type assumptions. Elliptic transmission and two-dimensional Navier-Stokes experiments assess parameter and state reconstruction, noise and scalarization effects, and PINN/XPINN references. Ablations show that removing state interaction while retaining aggregation deteriorates parameter recovery in the tested configurations, particularly for Navier-Stokes.
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BibTeX
@misc{biccari2026bihyco,
title = {{Bi-HYCO: Bi-Objective Cooperative Learning for PDE Parameter Identification under Fragmented Observations}},
author = {Umberto Biccari and Jun Chen and Roberto Morales and Enrique Zuazua},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06511},
eprint = {2609.06511},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06511},
}
RIS
TY - UNPB
TI - Bi-HYCO: Bi-Objective Cooperative Learning for PDE Parameter Identification under Fragmented Observations
AU - Umberto Biccari
AU - Jun Chen
AU - Roberto Morales
AU - Enrique Zuazua
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06511
UR - https://arxiv.org/abs/2609.06511
AB - Physical and synthetic models may describe complementary aspects of the same PDE-governed system while receiving different, possibly fragmented, observations. We propose Bi-Objective HYCO (Bi-HYCO), a cooperative framework that retains both representations and their local observational objectives while coupling their predicted states at unlabeled interaction points. These points contain no measurements and do not augment the data; they provide a communication mechanism in the common state space. The two criteria form a vector-valued objective, and weighted scalarizations provide computational realizations. For the deterministic shared-observation algorithm with fixed interaction points, we prove sufficient decrease and finite length of the whole alternating sequence, which converges to a mixed critical point under the stated Kurdyka-Lojasiewicz-type assumptions. Elliptic transmission and two-dimensional Navier-Stokes experiments assess parameter and state reconstruction, noise and scalarization effects, and PINN/XPINN references. Ablations show that removing state interaction while retaining aggregation deteriorates parameter recovery in the tested configurations, particularly for Navier-Stokes.
ER -