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Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…

Couplings in complex real-world systems are often nonlinear and scale-dependent. In many cases, it is crucial to consider a multitude of interlinked variables and the strengths of their correlations to adequately fathom the dynamics of a…

We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete…

Nonlinear dynamical systems with regime transitions are typically described by ordinary differential equations with jumping parameters parameters. Traditional methods often treat change-point detection and parameter estimation as separate…

An approach for the identification of discontinuous and nonsmooth nonlinear forces, as those generated by frictional contacts, in mechanical systems that can be approximated by a single-degree-of-freedom model is presented. To handle the…

We extend the model-free Data-Driven computing paradigm to solids and structures that are stochastic due to intrinsic randomness in the material behavior. The behavior of such materials is characterized by a likelihood measure instead of a…

Inferring structural connectivity from observed dynamics remains a fundamental open problem in complex systems, particularly for nonlinear networks where direct measurements are unavailable, and existing methodological approaches each incur…

A common objective in the analysis of tabular data is estimating the conditional distribution (in contrast to only producing predictions) of a set of "outcome" variables given a set of "covariates", which is sometimes referred to as the…

In this paper, we propose a covariate-adjusted nonlinear regression model. In this model, both the response and predictors can only be observed after being distorted by some multiplicative factors. Because of nonlinearity, existing methods…

Physics-informed neural networks have emerged as an alternative method for solving partial differential equations. However, for complex problems, the training of such networks can still require high-fidelity data which can be expensive to…

We propose a novel differentiable physics engine for system identification of complex spring-rod assemblies. Unlike black-box data-driven methods for learning the evolution of a dynamical system \emph{and} its parameters, we modularize the…

Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is to use a neural network as a global ansatz function to partial…

Effective and causal observable functions for low-order lifting linearization of nonlinear controlled systems are learned from data by using neural networks. While Koopman operator theory allows us to represent a nonlinear system as a…

In the wild, we often encounter collections of sequential data such as electrocardiograms, motion capture, genomes, and natural language, and sequences may be multichannel or symbolic with nonlinear dynamics. We introduce a new method to…

In the framework of solid mechanics, the task of deriving material parameters from experimental data has recently re-emerged with the progress in full-field measurement capabilities and the renewed advances of machine learning. In this…

This work focuses on developing a data-driven framework using Koopman operator theory for system identification and linearization of nonlinear systems for control. Our proposed method presents a deep learning framework with recursive…

Identifying causal relationships from observational time series data is a key problem in disciplines such as climate science or neuroscience, where experiments are often not possible. Data-driven causal inference is challenging since…

The problem of estimating an unknown force driving a linear oscillator is revisited. When using linear measurement, feedback is often cited as a mechanism to enhance bandwidth or sensitivity. We show that as long as the oscillator dynamics…

Many mathematical modelling tasks (such as in Economics and Finance) are informed by data that is "found" rather than being the result of carefully designed experiments. This often results in data series that are short, noisy,…

While linear systems have been useful in solving problems across different fields, the need for improved performance and efficiency has prompted them to operate in nonlinear modes. As a result, nonlinear models are now essential for the…