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In order to extract governing equations from time-series data, various approaches are proposed. Among those, sparse identification of nonlinear dynamics (SINDy) stands out as a successful method capable of modeling governing equations with…

Neural compression is the application of neural networks and other machine learning methods to data compression. Recent advances in statistical machine learning have opened up new possibilities for data compression, allowing compression…

Although deep neural networks and in particular Convolutional Neural Networks have demonstrated state-of-the-art performance in image classification with relatively high efficiency, they still exhibit high computational costs, often…

Accurate estimation of error covariances (both background and observation) is crucial for efficient observation compression approaches in data assimilation of large-scale dynamical problems. We propose a new combination of a covariance…

We analyze the convergence of compressive sensing based sampling techniques for the efficient evaluation of functionals of solutions for a class of high-dimensional, affine-parametric, linear operator equations which depend on possibly…

We prove that stochastic gradient descent (SGD) finds a solution that achieves $(1-\epsilon)$ classification accuracy on the entire dataset. We do so under two main assumptions: (1. Local progress) The model accuracy improves on average…

We propose a kernel compression method for solving Distributed-Order (DO) Fractional Partial Differential Equations (DOFPDEs) at the cost of solving corresponding local-in-time PDEs. The key concepts are (1) discretization of the integral…

The Kolmogorov-Smirnov (KS) test is a nonparametric statistical test used to test for differences between univariate probability distributions. The versatility of the KS test has made it a cornerstone of statistical analysis across many…

We present a compressive sensing approach for the long standing problem of Matsubara summation in many-body perturbation theory. By constructing low-dimensional, almost isometric subspaces of the Hilbert space we obtain optimum imaginary…

Lossy compressors are increasingly adopted in scientific research, tackling volumes of data from experiments or parallel numerical simulations and facilitating data storage and movement. In contrast with the notion of entropy in lossless…

We investigate the performance of entropy estimation methods, based either on block entropies or compression approaches, in the case of bidimensional sequences. We introduce a validation dataset made of images produced by a large number of…

Analyzing and controlling system entropy is a powerful tool for regulating predictability of control systems. Applications benefiting from such approaches range from reinforcement learning and data security to human-robot collaboration. In…

We present a new algorithm for isothermal-isobaric molecular-dynamics simulation. The method uses an extended Hamiltonian with an Andersen piston combined with the Nos'e-Poincar'e thermostat, recently developed by Bond, Leimkuhler and Laird…

Kolmogorov-Arnold Networks have emerged as interpretable alternatives to traditional multi-layer perceptrons. However, standard implementations lack principled uncertainty quantification capabilities essential for many scientific…

Polydisperse systems are commonly encountered when dealing with soft matter in general or any non simple fluid. Yet their treatment within the framework of statistical thermodynamics is a delicate task as the latter has been essentially…

We show that several classical quantities controlling compressed sensing performance directly match classical parameters controlling algorithmic complexity. We first describe linearly convergent restart schemes on first-order methods…

In this paper, we present the Monte-Carlo Compressive Optimization algorithm, a new method to solve a combinatorial optimization problem that is assumed compressible. The method relies on random queries to the objective function in order to…

Seismic inversion and imaging are adjoint-based optimization problems that process up to terabytes of data, regularly exceeding the memory capacity of available computers. Data compression is an effective strategy to reduce this memory…

This work approximates high-dimensional density functions with an ANOVA-like sparse structure by the mixture of wrapped Gaussian and von Mises distributions. When the dimension $d$ is very large, it is complex and impossible to train the…

Several powerful machines, such as the D-Wave 2000Q, dedicated to solving combinatorial optimization problems through the Ising-model formulation have been developed. To input problems into the machines, the unknown parameters on the Ising…