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On the physical
interpretation of neural PDEs
Sauro Succi |
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Vol. 13 (2025), No. 3, 275–286
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DOI: 10.2140/memocs.2025.13.275
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Abstract |
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We highlight a formal and substantial analogy between machine learning (ML) algorithms and discrete dynamical systems (DDS) in relaxation form. The analogy offers a transparent interpretation of the weights in terms of physical information-propagation processes and identifies the model function of the forward ML step with the local attractor of the corresponding discrete dynamics. Besides improving the explainability of current ML applications, this analogy may also facilitate the development of a new class ML algorithms with a reduced number of weights. |
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Keywords
machine learning, partial differential equations, discrete
dynamical systems
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Mathematical Subject Classification
Primary: 35Axx, 44Axx, 68Txx
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Milestones
Received: 9 February 2025
Accepted: 23 March 2025
Published: 6 September 2025
Communicated by Roberto Natalini
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Authors |
| Sauro Succi | ||
| Italian Institute of
Technology 00161 Rome Italy |
CNR-IAC 00185, Roma Italy |
Physics Department Harvard University Cambridge, MA United States |
| © 2025 MSP (Mathematical Sciences Publishers). |
