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Gradient-Update Mismatch: Rethinking Conflict-Free Training of Physics-Informed Neural Networks

arXiv · AI, language, vision and robotics · article · Sep 1, 2026 · UTC

Training Physics-Informed Neural Networks (PINNs) requires jointly optimizing physics residual and initial/boundary condition loss terms, which often induce conflicting gradients. Gradient surgery methods mitigate this issue by constructing directions from loss-specific gradients to reduce conflict before optimizer transformation. However, even when the constructed direction is conflict-free, this property may not be preserved after optimizer transformation. Let $a_t$ denote the direction constructed by gradient surgery, $u_t$ the optimizer proposal, and $\mathcal{C}_t$ the conflict-free cone

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