Extrapolation and learning equations

Abstract

In classical machine learning, regression is treated as a black box process of identifying a suitable function from a hypothesis set without attempting to gain insight into the mechanism connecting inputs and outputs. In the natural sciences, however, finding an interpretable function for a phenomenon is the prime goal as it allows to understand and generalize results. This paper proposes a novel type of function learning network, called equation learner (EQL), that can learn analytical expressions and is able to extrapolate to unseen domains. It is implemented as an end-to-end differentiable feed-forward network and allows for efficient gradient based training. Due to sparsity regularization concise interpretable expressions can be obtained. Often the true underlying source expression is identified.

13 pages, 8 figures, 4 tables

Cited by in corpus (8)

• Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery
• Extrapolation of nuclear structure observables with artificial neural networks
• SymbolicGPT: A Generative Transformer Model for Symbolic Regression
• Data-Driven Discovery of Coarse-Grained Equations
• Neural Status Registers
• CTSR: Cartesian tensor-based sparse regression for data-driven discovery of high-dimensional invariant governing equations
• Physics-informed Spline Learning for Nonlinear Dynamics Discovery
• Toward Neural-Network-Guided Program Synthesis and Verification