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Directional motion towards a specified destination is a common occurrence in physical processes and human societal activities. Utilizing this prior information can significantly improve the control and predictive performance of system…
Gaussian Mixture Models (GMM) do not adapt well to curved and strongly nonlinear data. However, we can use Gaussians in the curvilinear coordinate systems to solve this problem. Moreover, such a solution allows for the adaptation of…
Machine-learning based methods like physics-informed neural networks and physics-informed neural operators are becoming increasingly adept at solving even complex systems of partial differential equations. Boundary conditions can be…
The existence of generalized steady states (GSSs) in nonlinear mechanical systems under moderate temporally aperiodic forcing has only been shown recently. Here we derive systematic expansions for such GSSs and construct a numerical…
Global climate models represent small-scale processes such as clouds and convection using quasi-empirical models known as parameterizations, and these parameterizations are a leading cause of uncertainty in climate projections. A promising…
Lubricated friction is a multiscale problem where molecular processes dictate the macroscopic response of the system. Traditional lubrication models rely on semi-empirical constitutive relations, which become unreliable under extreme…
We describe how physical universes that are composed of gauge and gravitationally interacting bosonic and fermionic quantum fields arise from the generic discrete distribution of many quantifiable properties of arbitrary static entities.…
Many processes in chemistry and physics take place on timescales that cannot be explored using standard molecular dynamics simulations. This renders the use of enhanced sampling mandatory. Here we introduce an enhanced sampling method that…
In this Ph.D. thesis, we study the methods to constrain particle physics models using the stochastic GW imprints from cosmological phase transitions (PTs). Beginning with the theory and background, we describe how the GW background from…
We extend the restrictiveness measure of Fudenberg, Gao & Liang (2026) to functional and structural econometric settings using Gaussian process priors. We find that models evaluated over continuum domains appear more restrictive than when…
In this work, a new class of vector-valued phase field models is presented, where the values of the phase parameters are constrained by a convex set. The generated phase fields feature the partition of the domain into patches of distinct…
We have implemented quantum modeling mainly based on Bohmian Mechanics to study time series that contain strong coupling between their events. We firstly propose how compared to normal densities, our target time series seem to be associated…
Learning for control in repeated tasks allows for well-designed experiments to gather the most useful data. We consider the setting in which we use a data-driven controller that does not have access to the true system dynamics. Rather, the…
Graph diffusion models have emerged as state-of-the-art techniques in graph generation; yet, integrating domain knowledge into these models remains challenging. Domain knowledge is particularly important in real-world scenarios, where…
Anomalous diffusion is an established phenomenon but still a theoretical challenge in non-equilibrium statistical mechanics. Physical models are built incrementally, and the most recent and most general family is based on the fractional…
Uncertainty-aware robot motion prediction is crucial for downstream traversability estimation and safe autonomous navigation in unstructured, off-road environments, where terrain is heterogeneous and perceptual uncertainty is high. Most…
We study the law of a random field $f_N(\boldsymbol{\sigma})$ evaluated at a random sample from the Gibbs measure associated to a Gaussian field $H_N(\boldsymbol{\sigma})$. In the high-temperature regime, we show that bounds on the…
Discrete Markov random fields form a natural class of models to represent images and spatial data sets. The use of such models is, however, hampered by a computationally intractable normalising constant. This makes parameter estimation and…
One of the most criticized features of Bayesian statistics is the fact that credible intervals, especially when open likelihoods are involved, may strongly depend on the prior shape and range. Many analyses involving open likelihoods are…
Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are sample efficient, and interpretable but often rely on rigid assumptions. Furthermore, direct numerical approximation…