From Well-Posed Inversion to Learning Design: Physics- Informed Neural Estimation for Autonomic Regulation

Summary

arXiv:2606.03679v1 Announce Type: new Abstract: Learning-based and physics-informed methods are increasingly used for inverse estimation in controlled nonlinear dynamical systems. However, in many such approaches, the theoretic requirements that make unknown-input reconstruction meaningful, namely well-posedness in the sense of Hadamard, are often disregarded or weakly addressed through generic regularization terms with no explicit guarantees. In this work, we adopt a complementary viewpoint in which these control-theoretic and structural conditions inform the estimator design and constrain its training.