Loss Landscape Diagnosis for Gradient-Based Gray-Scott System Inversion: Disentangling the Roles of PINN Components
arXiv:2606.11258v1 Announce Type: new Abstract: Gradient-based inversion of reaction-diffusion systems is typically approached via surrogate models or physics-informed neural networks (PINNs), while the most direct route, backpropagation through the PDE's structure itself, has largely been avoided. We pursue this direct route as a diagnostic probe, backpropagating a steady-state loss through unrolled Gray-Scott simulation to recover its parameters, with no surrogate or neural-network augmentation. Optimization fails to converge, and plotting the landscape directly locates the failure in its ge
The proliferation of complex AI models and scientific computing demands more efficient and robust optimization techniques, making current limitations in gradient-based methods a timely focus.
Improving the diagnostic capabilities of AI optimization, especially for physics-informed neural networks and direct PDE inversion, can unlock new efficiencies and solve previously intractable problems in scientific modeling.
Understanding the 'loss landscape' for gradient-based inversion without surrogates could lead to more robust and explainable AI models for scientific discovery, moving beyond black-box approaches.
- · AI researchers
- · computational scientists
- · scientific modeling software developers
- · developers of less explainable surrogate models
- · inefficient black-box optimization techniques
This research provides deeper insight into the failure modes of gradient-based optimization for complex physical systems.
Improved diagnostic tools could accelerate the development of more stable and effective Physics-Informed Neural Networks.
Better understanding of AI optimization landscapes could lead to breakthroughs in areas like materials science, drug discovery, and climate modeling, where complex PDEs are fundamental.
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Read at arXiv cs.LG