Related papers: Equation discovery framework EPDE: Towards a bette…
We consider the data-driven discovery of governing equations from time-series data in the limit of high noise. The algorithms developed describe an extensive toolkit of methods for circumventing the deleterious effects of noise in the…
We propose a machine learning framework to accelerate numerical computations of time-dependent ODEs and PDEs. Our method is based on recasting (generalizations of) existing numerical methods as artificial neural networks, with a set of…
The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery ($\text{S}^3\text{d}$), decides which…
As a cornerstone in the Evolutionary Computation (EC) domain, Differential Evolution (DE) is known for its simplicity and effectiveness in handling challenging black-box optimization problems. While the advantages of DE are well-recognized,…
In this work, we present an adjoint-based method for discovering the underlying governing partial differential equations (PDEs) given data. The idea is to consider a parameterized PDE in a general form and formulate a PDE-constrained…
Experienced users often have useful knowledge and intuition in solving real-world optimization problems. User knowledge can be formulated as inter-variable relationships to assist an optimization algorithm in finding good solutions faster.…
Discovering efficient algorithms for solving complex problems has been an outstanding challenge in mathematics and computer science, requiring substantial human expertise over the years. Recent advancements in evolutionary search with large…
Most common mechanistic models are traditionally presented in mathematical forms to explain a given physical phenomenon. Machine learning algorithms, on the other hand, provide a mechanism to map the input data to output without explicitly…
Our ability to predict, control, and ultimately understand complex systems rests on discovering the equations that govern their dynamics. Identifying these equations directly from noisy, limited observations has therefore become a central…
Distilling data into compact and interpretable analytic equations is one of the goals of science. Instead, contemporary supervised machine learning methods mostly produce unstructured and dense maps from input to output. Particularly in…
Sparse model identification enables the discovery of nonlinear dynamical systems purely from data; however, this approach is sensitive to noise, especially in the low-data limit. In this work, we leverage the statistical approach of…
Discovering interpretable mathematical equations from observed data (a.k.a. equation discovery or symbolic regression) is a cornerstone of scientific discovery, enabling transparent modeling of physical, biological, and economic systems.…
Model discovery aims to uncover governing differential equations of dynamical systems directly from experimental data. Benchmarking such methods is essential for tracking progress and understanding trade-offs in the field. While prior…
Despite large incentives, ecorrectness in software remains an elusive goal. Declarative programming techniques, where algorithms are derived from a specification of the desired behavior, offer hope to address this problem, since there is a…
With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics…
In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…
Equation discovery is a fundamental learning task for uncovering the underlying dynamics of complex systems, with wide-ranging applications in areas such as brain connectivity analysis, climate modeling, gene regulation, and physical…
We propose a novel information-theoretic approach for Bayesian optimization called Predictive Entropy Search (PES). At each iteration, PES selects the next evaluation point that maximizes the expected information gained with respect to the…
This work is concerned with discovering the governing partial differential equation (PDE) of a physical system. Existing methods have demonstrated the PDE identification from finite observations but failed to maintain satisfying results…
Accurately modeling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data.…