Complexity Methods in Physics-Guided Machine Learning
- Authors
- Publication Date
- Dec 20, 2023
- Source
- HAL-Descartes
- Keywords
- Language
- English
- License
- Unknown
- External links
Abstract
Complexity is easy to recognize but difficult to define: there are a host of measures of complexity, each relevant for a particular application.In Surface engineering, self-organization drives the formation of patterns on matter by femtosecond laser irradiation, which have important biomedical applications. Pattern formation details are not fully understood. In work leading to two publications [1,2], via a complexity argument and a physics-guided machine learning framework, we show that the severely constrained problem of learning the laser-matter interaction with few data and partial physical knowledge is well-posed in this context. Our model allows us to make useful predictions and suggests physical insights.In another contribution [3] we propose a new formulation of the Minimum Description Length principle, defining model and data complexity in a single step, by taking into account signal and noise in training data. Experiments indicate that Neural Network classifiers that generalize well follow this principle.In unpublished work, we propose Taylor entropy, a novel measure of dynamical system complexity which can be estimated via a single SEM image. This approach could facilitate learning the physical process in new materials through domain adaptation.This thesis paves the way for a unified representation of complexity in data and physical knowledge, which can be used in the context of Physics-guided machine learning.[1] Brandao, Eduardo, et al. "Learning PDE to model self-organization of matter." Entropy 24.8 (2022): 1096.[2] Brandao, Eduardo, et al. "Learning Complexity to Guide Light-Induced Self-Organized Nanopatterns." Physical Review Letters 130.22 (2023): 226201.[3] Brandao, Eduardo, et al. "Is My Neural Net Driven by the MDL Principle?." Joint European Conference on Machine Learning and Knowledge Discovery in Databases. Cham: Springer Nature Switzerland, 2023.
