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Discussion of Probabilistic Learning
As the previous sections have demonstrated, probabilistic learning offers a wide range of very exciting possibilities in the context of physics-based learning. First, these methods come with a highly interesting and well developed theory. Surprisingly, some parts are actually more developed than basic questions about simpler learning approaches.
At the same time, they enable a fundamentally different way to work with simulations: they provide a simple way to work with complex distributions of solutions. This is of huge importance for inverse problems, e.g. in the context of obtaining likelihood-based estimates for simulation-based inference.
That being said, diffusion based approaches will not show relatively
few advantages for deterministic settings: they are not more accurate,
and typically induce slightly larger computational costs. An interesting
exception is the long-term stability, as discussed in
{doc}probmodels-uncond. To summarize the key aspects of
probabilistic deep learning approaches:
✅ Pro: - Enable training and inference for distributions - Well developed theory - Stable training
❌ Con: - (Slightly) increased inference cost - No real advantage for deterministic settings
One more concluding recommendation: if your problems contains ambiguities, diffusion modeling in the form of flow matching is the method of choice. If your data contains reliable input-output pairs, go with simpler deterministic training instead.
Next, we can turn to a new viewpoint on learning problems, the field of reinforcement learning. As the next sections will point out, it is actually not so different from the topics of the previous chapters despite the new viewpoint.