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Adapting large-scale foundation models to new domains with limited supervision remains a fundamental challenge due to latent distribution mismatch, unstable optimization dynamics, and miscalibrated uncertainty propagation. This paper…
Optimal Bayesian design techniques provide an estimate for the best parameters of an experiment in order to maximize the value of measurements prior to the actual collection of data. In other words, these techniques explore the space of…
Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) are fundamental for modeling stochastic dynamics across the natural sciences and modern machine learning. Learning their solution operators with…
Variational Autoencoders (VAEs) provide a flexible and scalable framework for non-linear dimensionality reduction. However, in application domains such as genomics where data sets are typically tabular and high-dimensional, a black-box…
Variational autoencoders (VAEs), as well as other generative models, have been shown to be efficient and accurate for capturing the latent structure of vast amounts of complex high-dimensional data. However, existing VAEs can still not…
High-energy collisions at the Large Hadron Collider (LHC) provide valuable insights into open questions in particle physics. However, detector effects must be corrected before measurements can be compared to certain theoretical predictions…
Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image…
We present a regression technique for data-driven problems based on polynomial chaos expansion (PCE). PCE is a popular technique in the field of uncertainty quantification (UQ), where it is typically used to replace a runnable but expensive…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
Matrix models are a highly successful framework for the analytic study of random two dimensional surfaces with applications to quantum gravity in two dimensions, string theory, conformal field theory, statistical physics in random geometry,…
We present a novel way of deciding when and where to refine a mesh in probability space in order to facilitate the uncertainty quantification in the presence of discontinuities in random space. A discontinuity in random space makes the…
We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…
Stabilizing unstable periodic orbits in a chaotic invariant set not only reveals information about its structure but also leads to various interesting applications. For the successful application of a chaos control scheme, convergence speed…
Two recent papers on prediction of chaotic systems, one on multi-view embedding1 , and the second on prediction in projection2 provide empirical evidence to support particular prediction methods for chaotic systems. Multi-view embedding1 is…
The ability to accurately model random fields plays a critical role in science and engineering for problems involving uncertain, spatially-varying quantities such as heterogeneous material properties and turbulent flows. Deep generative…
Polynomial chaos expansions (PCE) allow us to propagate uncertainties in the coefficients of differential equations to the statistics of their solutions. Their main advantage is that they replace stochastic equations by systems of…
Black box variational inference allows researchers to easily prototype and evaluate an array of models. Recent advances allow such algorithms to scale to high dimensions. However, a central question remains: How to specify an expressive…
Spatiotemporal chaotic systems are difficult to characterize in a model-free manner because of their high dimensionality, strong nonlinearity, and sensitivity to initial conditions. Coupled map lattices, as a representative class of…
We consider the problem of variational Bayesian inference in a latent variable model where a (possibly complex) observed stochastic process is governed by the solution of a latent stochastic differential equation (SDE). Motivated by the…
This paper presents an innovative approach, the Adaptive Orthogonal Basis Method, tailored for computing multiple solutions to differential equations characterized by polynomial nonlinearities. Departing from conventional practices of…