Physics-Informed Neural Networks for Coupled Non-Isothermal Two-Phase Flow in Porous Media: Training Pathologies, Remedies, and the Role of Gradient Conflict

Abstract

Physics-informed neural networks (PINNs) are difficult to train on strongly coupled, multi-objective systems: with fixed loss weights an otherwise identical run succeeds or diverges with the random seed, and a leading explanation attributes the failures to conflict between the loss-term gradients. We test that explanation on a coupled non-isothermal Buckley–Leverett displacement with a passive tracer, a three-front hot-water flood with an exact analytical solution as ground truth. The test produces an exactly verified counterexample: the conflict-free update ConFIG attains its alignment objective yet converges to a stable solution that violates the equations, while a quasi-second-order optimizer (SOAP) and per-term gradient surgery (PCGrad) train the network reliably with no loss-weight search. The most aligned update is thus the one that fails: gradient alignment is neither necessary nor sufficient for trainability, and the conflict is a diagnostic of the loss rather than its cause. The same formulation serves the forward, parametric, and inverse problems: it predicts the movable-oil recovery with a relative error of about 5%, returns the solution for any oil viscosity in a trained range from one network, and, from sparse near-injector monitoring, recovers the thermal front speed and one transport coefficient when the other is known. To our knowledge this is the first PINN solution of this coupled displacement, which is central to thermal oil recovery.