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Magnetic Particle Imaging is an emerging imaging modality through which it is possible to detect tracers containing superparamagnetic nanoparticles. The exposure of the particles to dynamic magnetic fields generates a non-linear response…

Structured optical waveforms are emerging as powerful control fields for the next generation of complex photonic and electromagnetic systems, where the temporal structure of light can determine the ultimate performance of scientific…

Machine learning models can represent climate processes that are nonlocal in horizontal space, height, and time, often by combining information across these dimensions in highly nonlinear ways. While this can improve predictive skill, it…

Finding interpretable biomechanical models can provide insight into the functionality of organs with regard to physiology and disease. However, identifying broadly applicable dynamical models for in vivo tissue remains challenging. In this…

Deep learning is regarded as a promising solution for reversible steganography. There is an accelerating trend of representing a reversible steo-system by monolithic neural networks, which bypass intermediate operations in traditional…

While artificial neural networks excel in unsupervised learning of non-sparse structure, classical statistical regression techniques offer better interpretability, in particular when sparseness is enforced by $\ell_1$ regularization,…

Dynamical systems are ubiquitous within science and engineering, from turbulent flow across aircraft wings to structural variability of proteins. Although some systems are well understood and simulated, scientific imaging often confronts…

Despite strong empirical performance for image classification, deep neural networks are often regarded as ``black boxes'' and they are difficult to interpret. On the other hand, sparse convolutional models, which assume that a signal can be…

Predicting the dynamics of complex systems is crucial for various scientific and engineering applications. The accuracy of predictions depends on the model's ability to capture the intrinsic dynamics. While existing methods capture key…

The dynamics of neuron populations commonly evolve on low-dimensional manifolds. Thus, we need methods that learn the dynamical processes over neural manifolds to infer interpretable and consistent latent representations. We introduce a…

Probabilistic models with discrete latent variables naturally capture datasets composed of discrete classes. However, they are difficult to train efficiently, since backpropagation through discrete variables is generally not possible. We…

The present paper reviews recent advances in the theory of nonlinear driven magnetohydrodynamic (MHD) waves in slow and Alfven resonant layers. Simple estimations show that in the vicinity of resonant positions the amplitude of variables…

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…

Dictionary learning is the task of determining a data-dependent transform that yields a sparse representation of some observed data. The dictionary learning problem is non-convex, and usually solved via computationally complex iterative…

We present an algorithm to learn the relevant latent variables of a large-scale discretized physical system and predict its time evolution using thermodynamically-consistent deep neural networks. Our method relies on sparse autoencoders,…

Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…

We present a novel interpretable machine learning model to accurately predict complex rippling deformations of Multi-Walled Carbon Nanotubes(MWCNTs) made of millions of atoms. Atomistic-physics-based models are accurate but computationally…

Humans gain an implicit understanding of physical laws through observing and interacting with the world. Endowing an autonomous agent with an understanding of physical laws through experience and observation is seldom practical: we should…

This paper revisits building machine learning algorithms that involve interactions between entities, such as those between financial assets in an actively managed portfolio, or interactions between users in a social network. Our goal is to…

In this work, we derive reduced interface models for hydroelastic water waves coupled to a nonlinear viscoelastic plate. In a weakly nonlinear small-steepness regime we obtain bidirectional nonlocal evolution equations capturing the…