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Optimization Landscapes Learned: Proxy Networks Boost Convergence in Physics-based Inverse Problems

arXiv 2501.16573 ↗First posted 27 Jan 2025cs.LG math.OCcited by 0

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Abstract (arXiv)

Solving inverse problems in physics is central to understanding complex systems and advancing technologies in various fields. Iterative optimization algorithms, commonly used to solve these problems, often encounter local minima, chaos, or regions with zero gradients. This is due to their overreliance on local information and highly chaotic inverse loss landscapes governed by underlying partial differential equations (PDEs). In this work, we show that deep neural networks successfully replicate such complex loss landscapes through spatio-temporal trajectory inputs. They also offer the potential to control the underlying complexity of these chaotic loss landscapes during training through various regularization methods. We show that optimizing on network-smoothened loss landscapes leads to improved convergence in predicting optimum inverse parameters over conventional momentum-based optimizers such as BFGS on multiple challenging problems.

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References · 18

  1. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
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  12. 2018A Deep Neural Network Surrogate for High-Dimensional Random Partial Differential Equationscited by 23
6 more
  1. 2021Learning Regularization Parameters of Inverse Problems via Deep Neural Networkscited by 19
  2. 2020DeepCFD: Efficient Steady-State Laminar Flow Approximation with Deep Convolutional Neural Networkscited by 15
  3. 2021Inverse design of two-dimensional materials with invertible neural networkscited by 15
  4. 2018An Unsupervised Approach to Solving Inverse Problems using Generative Adversarial Networkscited by 7
  5. 2021Inversion of Integral Models: a Neural Network Approachcited by 2
  6. 2023Physics-informed neural network for seismic wave inversion in layered semi-infinite domaincited by 2

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