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Most common mechanistic models are traditionally presented in mathematical forms to explain a given physical phenomenon. Machine learning algorithms, on the other hand, provide a mechanism to map the input data to output without explicitly…

The application of deep learning toward discovery of data-driven models requires careful application of inductive biases to obtain a description of physics which is both accurate and robust. We present here a framework for discovering…

Accurate and efficient plasma models are essential to understand and control experimental devices. Existing magnetohydrodynamic or kinetic models are nonlinear, computationally intensive, and can be difficult to interpret, while often only…

The goal of dynamic magnetic resonance imaging (dynamic MRI) is to visualize tissue properties and their local changes over time that are traceable in the MR signal. We propose a new variational approach for the reconstruction of subsampled…

Dynamical systems models such as recurrent neural networks (RNNs) are increasingly popular in theoretical neuroscience for hypothesis-generation and data analysis. Evaluating the dynamics in such models is key to understanding their learned…

The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…

Many dynamical processes of complex systems can be understood as the dynamics of a group of nodes interacting on a given network structure. However, finding such interaction structure and node dynamics from time series of node behaviours is…

Discovering governing equations from data is crucial for understanding complex systems in many diverse fields from science to engineering. Yet, there still is a lack of versatile computational toolbox to deal with this long standing…

The development of biophysical models for clinical applications is rapidly advancing in the research community, thanks to their predictive nature and their ability to assist the interpretation of clinical data. However, high-resolution and…

Online system identification algorithms are widely used for monitoring, diagnostics and control by continuously adapting to time-varying dynamics. Typically, these algorithms consider a model structure that lacks parsimony and offers…

The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…

Reconstructing the equation of motion and thus the network topology of a system from time series is a very important problem. Although many powerful methods have been developed, it remains a great challenge to deal with systems in high…

This paper establishes a kernel-based framework for reconstructing data on manifolds, tailored to fit the dynamic-(d)MRI-data recovery problem. The proposed methodology exploits simple tangent-space geometries of manifolds in reproducing…

Discovering governing equations from observational data remains a fundamental challenge in scientific modeling, particularly when the underlying mathematical structure is unknown. Traditional sparse identification methods like SINDy excel…

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…

First principles modeling of physical systems has led to significant technological advances across all branches of science. For nonlinear systems, however, small modeling errors can lead to significant deviations from the true, measured…

In dynamic positron emission tomography (PET) reconstruction, the importance of leveraging the temporal dependence of the data has been well appreciated. Current deep-learning solutions can be categorized in two groups in the way the…

Hybrid systems are traditionally difficult to identify and analyze using classical dynamical systems theory. Moreover, recently developed model identification methodologies largely focus on identifying a single set of governing equations…

This paper concerns the data-driven sensor deployment problem in large spatiotemporal fields. Traditionally, sensor deployment strategies have been heavily dependent on model-based planning approaches. However, model-based approaches do not…

Dynamic MRI enables a range of clinical applications, including cardiac function assessment, organ motion tracking, and radiotherapy guidance. However, fully sampling the dynamic k-space data is often infeasible due to time constraints and…