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Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

Predicting the response of nonlinear dynamical systems subject to random, broadband excitation is important across a range of scientific disciplines, such as structural dynamics and neuroscience. Building data-driven models requires…

The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…

We develop a method for reconstructing regulatory interconnection networks between variables evolving according to a linear dynamical system. The work is motivated by the problem of gene regulatory network inference, that is, finding causal…

Automatic machine learning of empirical models from experimental data has recently become possible as a result of increased availability of computational power and dedicated algorithms. Despite the successes of non-parametric inference and…

We evaluate the robustness of a probabilistic formulation of system identification (ID) to sparse, noisy, and indirect data. Specifically, we compare estimators of future system behavior derived from the Bayesian posterior of a learning…

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity promoting…

Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. We…

Recent progress in autoencoder-based sparse identification of nonlinear dynamics (SINDy) under $\ell_1$ constraints allows joint discoveries of governing equations and latent coordinate systems from spatio-temporal data, including simulated…

Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing…

Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…

The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general…

Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep…

System identification of complex and nonlinear systems is a central problem for model predictive control and model-based reinforcement learning. Despite their complexity, such systems can often be approximated well by a set of linear…

In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…

In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…

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…

The focus in this paper is Bayesian system identification based on noisy incomplete modal data where we can impose spatially-sparse stiffness changes when updating a structural model. To this end, based on a similar hierarchical sparse…