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This research advances Physically Recurrent Neural Networks by introducing architectural constraints that simultaneously enhance latent space interpretability and enforce thermodynamic consistency. By leveraging adjoint encoder-decoder structures and weight normalization, the approach achieves robust training in low-data regimes while ensuring energy conservation across scales. These findings demonstrate how embedding physical laws directly into neural network design can significantly improve data efficiency without increasing model complexity.
On architectural choices for interpretability and thermodynamic consistency in Physically Recurrent Neural Networks in the low-data regime
arXiv:2610.04067v1 Announce Type: new Abstract: In this paper, we unravel the effect of different decoder architectures on the interpretability of the latent space of the Physically Recurrent Neural Network. Particular emphasis is given to a new weight normalization constraint, which acts as a regularization technique and enables robust training in the low-data regime. A brief visual exploration illustrates how these changes impact the latent space and how the fictitious stress can align with the true state of the RVE without explicit training. Reaping the benefits of a meaningful latent space, a case study illustrates how information from the microscopic level can be retrieved and incorporated into a multi-task approach that does not require extra parameters or larger training sets. Another key contribution shows that a specific architectural choice can naturally lead to a thermodynamically consistent formulation. By enforcing an adjoint encoder-decoder structure with positive scalar contributions, this modification ensures energy consistency across scales and non-negative dissipation, leading to even lower training requirements. This alternative completes the study on interpretability, inductive bias, and thermodynamic consistency, and demonstrates that data efficiency can be improved with careful architectural choices rooted in the underlying physics.
Abstract:In this paper, we unravel the effect of different decoder architectures on the interpretability of the latent space of the Physically Recurrent Neural Network. Particular emphasis is given to a new weight normalization constraint, which acts as a regularization technique and enables robust training in the low-data regime. A brief visual exploration illustrates how these changes impact the latent space and how the fictitious stress can align with the true state of the RVE without explicit training. Reaping the benefits of a meaningful latent space, a case study illustrates how information from the microscopic level can be retrieved and incorporated into a multi-task approach that does not require extra parameters or larger training sets. Another key contribution shows that a specific architectural choice can naturally lead to a thermodynamically consistent formulation. By enforcing an adjoint encoder-decoder structure with positive scalar contributions, this modification ensures energy consistency across scales and non-negative dissipation, leading to even lower training requirements. This alternative completes the study on interpretability, inductive bias, and thermodynamic consistency, and demonstrates that data efficiency can be improved with careful architectural choices rooted in the underlying physics.
Machine Learning (cs.LG); Numerical Analysis (math.NA)
arXiv:2610.04067 [cs.LG]
(or arXiv:2610.04067v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.04067 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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