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Learning processes by exploiting restricted domain knowledge is an important task across a plethora of scientific areas, with more and more hybrid training methods additively combining data-driven and model-based approaches. Although the…

Models play an essential role in the design process of cyber-physical systems. They form the basis for simulation and analysis and help in identifying design problems as early as possible. However, the construction of models that comprise…

This work presents a hybrid modeling approach to data-driven learning and representation of unknown physical processes and closure parameterizations. These hybrid models are suitable for situations where the mechanistic description of…

Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…

This work proposes a machine-learning framework for modeling the error incurred by approximate solutions to parameterized dynamical systems. In particular, we extend the machine-learning error models (MLEM) framework proposed in Ref. 15 to…

A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the physical processes governing the dynamics to build an approximate mathematical model of the system. In contrast, machine learning techniques have…

We propose a hybrid meta-learning framework for forecasting and anomaly detection in nonlinear dynamical systems characterized by nonstationary and stochastic behavior. The approach integrates a physics-inspired simulator that captures…

We present a data-driven modeling strategy to overcome improperly modeled dynamics for systems exhibiting complex spatio-temporal behaviors. We propose a Deep Learning framework to resolve the differences between the true dynamics of the…

We consider the problem of learning the dynamics of a linear system when one has access to data generated by an auxiliary system that shares similar (but not identical) dynamics, in addition to data from the true system. We use a weighted…

The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system…

A critical challenge in the data-driven modeling of dynamical systems is producing methods robust to measurement error, particularly when data is limited. Many leading methods either rely on denoising prior to learning or on access to large…

Machine learning offers an intriguing alternative to first-principles analysis for discovering new physics from experimental data. However, to date, purely data-driven methods have only proven successful in uncovering physical laws…

This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques. The proposed framework reformulates the prediction problem as a supervised learning problem to…

To predict rare extreme events using deep neural networks, one encounters the so-called small data problem because even long-term observations often contain few extreme events. Here, we investigate a model-assisted framework where the…

We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is in the form of noisy partial measurements of the past and present state of the dynamical system. Recently there have been several…

Extracting predictive models from nonlinear systems is a central task in scientific machine learning. One key problem is the reconciliation between modern data-driven approaches and first principles. Despite rapid advances in machine…

Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and…

In data-driven modelling of complex dynamic processes, it is often desirable to combine different classes of models to enhance performance. Examples include coupled models of different fidelities, or hybrid models based on physical…

The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations.…

Identifying a linear system model from data has wide applications in control theory. The existing work on finite sample analysis for linear system identification typically uses data from a single system trajectory under i.i.d random inputs,…