30 lines
1.2 KiB
Markdown
30 lines
1.2 KiB
Markdown
Discussion
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=======================
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In a way, the learning via physical gradients provides the tightest possible coupling
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of physics and NNs: the full non-linear process of the PDE model directly steers
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the optimization of the NN.
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Naturally, this comes at a cost - invertible simulators are more difficult to build
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(and less common) than the first-order gradients which are relatively commonly used
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for learning processes and adjoint optimizations. Nonetheless, if they're available,
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they can speed up convergence, and yield models that have an inherently better performance.
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Thus, once trained, these models can give a performance that we simply can't obtain
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by, e.g., training longer with a simpler approach. So, if we plan to evaluate these
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models often (e.g., ship them in an application), this increased one-time cost
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can pay off in the long run.
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## Summary
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✅ Pro:
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- Very accurate "gradient" information for learning and optimization.
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- Improved convergence and model performance.
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- Tightest possible coupling of model PDEs and learning.
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❌ Con:
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- Requires inverse simulators (at least local ones).
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- less wide-spread availability than, e.g., differentiable physics simulators.
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