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Many real world systems exhibit a quasi linear or weakly nonlinear behavior during normal operation, and a hard saturation effect for high peaks of the input signal. In this paper, a methodology to identify a parsimonious discrete-time…

Real-time nonlinear Bayesian filtering algorithms are overwhelmed by data volume, velocity and increasing complexity of computational models. In this paper, we propose a novel ensemble based nonlinear Bayesian filtering approach which only…

Nonlinear dynamical systems with input delays pose significant challenges for prediction, estimation, and control due to their inherent complexity and the impact of delays on system behavior. Traditional linear control techniques often fail…

The identification of repeating patterns in discrete grids is rudimentary within symbolic reasoning, algorithm synthesis and structural optimization across diverse computational domains. Although statistical approaches targeting noisy data…

Optimizing and certifying the positivity of polynomials are fundamental primitives across mathematics and engineering applications, from dynamical systems to operations research. However, solving these problems in practice requires large…

Recent work has used deep learning to derive symmetry transformations, which preserve conserved quantities, and to obtain the corresponding algebras of generators. In this letter, we extend this technique to derive sparse representations of…

Numerical modeling of different structural materials that have highly nonlinear behaviors has always been a challenging problem in engineering disciplines. Experimental data is commonly used to characterize this behavior. This study aims to…

This paper addresses the problem of estimating causal directed acyclic graphs in linear non-Gaussian acyclic models with latent confounders (LvLiNGAM). Existing methods assume mutually independent latent confounders or cannot properly…

A significant challenge in many fields of science and engineering is making sense of time-dependent measurement data by recovering governing equations in the form of differential equations. We focus on finding parsimonious ordinary…

Learning nonlinear dynamics from diffusion data is a challenging problem since the individuals observed may be different at different time points, generally following an aggregate behaviour. Existing work cannot handle the tasks well since…

A symbolic computational algorithm which detects " linear "` solutions of nonlinear polynomial differential equations of single functions, is developed throughout this paper.

In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system…

The logarithmic representation of infinitesimal generators is generalized to the cases when the evolution operator is unbounded. The generalized result is applicable to the representation of infinitesimal generators of unbounded evolution…

Understanding the dynamics of neural network parameters during training is one of the key challenges in building a theoretical foundation for deep learning. A central obstacle is that the motion of a network in high-dimensional parameter…

Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…

This paper addresses classification problems with matrix-valued data, which commonly arise in applications such as neuroimaging and signal processing. Building on the assumption that the data from each class follows a matrix normal…

The paper reports on a computer algebra program LSSS (Linear Selective Systems Solver) for solving linear algebraic systems with rational coefficients. The program is especially efficient for very large sparse systems that have a solution…

Equivariant machine learning is an approach for designing deep learning models that respect the symmetries of the problem, with the aim of reducing model complexity and improving generalization. In this paper, we focus on an extension of…

Discovering dynamical models to describe underlying dynamical behavior is essential to draw decisive conclusions and engineering studies, e.g., optimizing a process. Experimental data availability notwithstanding has increased…

Sparse inverse covariance estimation (i.e., edge de-tection) is an important research problem in recent years, wherethe goal is to discover the direct connections between a set ofnodes in a networked system based upon the observed…