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The SINDy algorithm has been successfully used to identify the governing equations of dynamical systems from time series data. However, SINDy assumes the user has prior knowledge of the variables in the system and of a function library that…
Modeling complex spatiotemporal dynamics, particularly in far-from-equilibrium systems, remains a grand challenge in science. The governing partial differential equations (PDEs) for these systems are often intractable to derive from first…
Deep learning models have achieved remarkable success in different areas of machine learning over the past decade; however, the size and complexity of these models make them difficult to understand. In an effort to make them more…
Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great…
We present a framework to train a structured prediction model by performing smoothing on the inference algorithm it builds upon. Smoothing overcomes the non-smoothness inherent to the maximum margin structured prediction objective, and…
Most decision tree induction algorithms are based on a greedy top-down recursive partitioning strategy for tree growth. In this paper, we propose several methods for induction of decision trees and their ensembles based on evolutionary…
We propose a novel data-driven method called QENDy (Quadratic Embedding of Nonlinear Dynamics) that not only allows us to learn quadratic representations of highly nonlinear dynamical systems, but also to identify the governing equations.…
Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically…
A novel simulation strategy is proposed to search for semiconductor quantum devices which are optimized with respect to required performances. Based on evolutionary programming, a tecnique implementing the paradigm of genetic algorithms to…
Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems.…
Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training…
Recently, machine learning methods have gained significant traction in scientific computing, particularly for solving Partial Differential Equations (PDEs). However, methods based on deep neural networks (DNNs) often lack convergence…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
In the present work, a multi-scale framework for neural network enhanced methods is proposed for approximation of function and solution of partial differential equations (PDEs). By introducing the multi-scale concept, the total solution of…
We propose an approach based on function evaluations and Bayesian inference to extract higher-order differential information of objective functions {from a given ensemble of particles}. Pointwise evaluation $\{V(x^i)\}_i$ of some potential…
The sparse identification of nonlinear dynamics (SINDy) approach can discover the governing equations of dynamical systems based on measurement data, where the dynamical model is identified as the sparse linear combination of the given…
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…
The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural networks to learn such data-driven partial differential…
We discuss a new optimization strategy, which considerably improves the effectivity of evolutionary algorithms applied to a certain class of optimization problems. The basic principle is to solve first a simpler related problem, which is…
Evidential Deep Learning (EDL) has emerged as an efficient, sampling-free strategy for uncertainty estimation. A series of EDL variants have been proposed to address specific limitations of the original framework, achieving notable success.…