Related papers: When Good Equations Get Bad Scores: Improving Symb…
We present a uniform analysis of biased stochastic gradient methods for minimizing convex, strongly convex, and non-convex composite objectives, and identify settings where bias is useful in stochastic gradient estimation. The framework we…
Particle-based modeling of materials at atomic scale plays an important role in the development of new materials and understanding of their properties. The accuracy of particle simulations is determined by interatomic potentials, which…
Describing the world behavior through mathematical functions help scientists to achieve a better understanding of the inner mechanisms of different phenomena. Traditionally, this is done by deriving new equations from first principles and…
This work designs a scalable, parameter-aware sparse regression framework for discovering interpretable partial differential equations and subgrid-scale closures from multi-parameter simulation data. Building on SINDy (Sparse Identification…
Analytical solutions to differential equations offer exact, interpretable insight but are rarely available because discovering them requires expert intuition or exhaustive search of combinatorial spaces. We introduce SIGS, a neuro-symbolic…
Despite successful seminal works on passive systems in the literature, learning free-form physical laws for controlled dynamical systems given experimental data is still an open problem. For decades, symbolic mathematical equations and…
Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network…
Discrete optimization problems often arise in deep learning tasks, despite the fact that neural networks typically operate on continuous data. One class of these problems involve objective functions which depend on neural networks, but…
Symbolic regression is essential for deriving interpretable expressions that elucidate complex phenomena by exposing the underlying mathematical and physical relationships in data. In this paper, we present an advanced symbolic regression…
We investigate the addition of constraints on the function image and its derivatives for the incorporation of prior knowledge in symbolic regression. The approach is called shape-constrained symbolic regression and allows us to enforce e.g.…
The reconstruction of particle tracks from hits in tracking detectors is a computationally intensive task due to the large combinatorics of detector signals. Recent efforts have proven that ML techniques can be successfully applied to the…
The goal in Symbolic Regression (SR) is to discover expressions that accurately map input to output data. Because often the intent is to understand these expressions, there is a trade-off between accuracy and the interpretability of…
Symbolic regression, a task discovering the formula best fitting the given data, is typically based on the heuristical search. These methods usually update candidate formulas to obtain new ones with lower prediction errors iteratively.…
Pre-trained seq2seq models excel at graph semantic parsing with rich annotated data, but generalize worse to out-of-distribution (OOD) and long-tail examples. In comparison, symbolic parsers under-perform on population-level metrics, but…
Automating scientific discovery has been a grand goal of Artificial Intelligence (AI) and will bring tremendous societal impact. Learning symbolic expressions from experimental data is a vital step in AI-driven scientific discovery. Despite…
The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…
Shape-constrained symbolic regression (SCSR) allows to include prior knowledge into data-based modeling. This inclusion allows to ensure that certain expected behavior is better reflected by the resulting models. The expected behavior is…
Relational data mining is becoming ubiquitous in many fields of study. It offers insights into behaviour of complex, real-world systems which cannot be modeled directly using propositional learning. We propose Symbolic Graph Embedding…
The Transformation-Interaction-Rational is a representation for symbolic regression that limits the search space of functions to the ratio of two nonlinear functions each one defined as the linear regression of transformed variables. This…
Feature selection aims to identify the optimal feature subset for enhancing downstream models. Effective feature selection can remove redundant features, save computational resources, accelerate the model learning process, and improve the…