Researchers develop new AI techniques to solve complex equations in physics (web.ub.edu)

Researchers from ICCUB and Harvard have introduced a new approach to physics-informed neural networks (PINNs) that combines multi-head (MH) training with a novel unimodular regularization (UR) to learn entire families of solutions rather than single-instance outputs. MH lets the network represent a solution manifold for a parameterized family of PDEs, while UR—motivated by concepts from differential geometry and ideas related to unimodular constraints—stabilizes training and improves generalization to harder regimes. The team demonstrates the method on three systems of increasing complexity (the flame equation, the Van der Pol oscillator, and holographic Einstein field equations), notably recovering unknown physical functions from synthetic data in the latter inverse-problem setting—something previously deemed nearly impossible. Technically, the paper shows that jointly training multiple heads to span a solution space, together with a regularizer that enforces geometric consistency, yields more robust and efficient PINNs compared with conventional single-solution networks and some traditional numerical solvers. The approach reduces training fragility in inverse tasks (where missing parameters or functions must be inferred) and extends the practical reach of PINNs for complex, data-driven discovery in physics. The work (Tarancón-Álvarez et al.) appears in Communications Physics (Aug 2025, DOI: 10.1038/s42005-025-02248-1).