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The objective of the paper is to investigate the approximate controllability property of a linear stochastic control system with values in a separable real Hilbert space. In a first step we prove the existence and uniqueness for the…
We study the elusive transition from exponential to post-exponential (algebraic) decay of the probability density of a quantum particle emitted by an exponentially decaying source, in one dimension. The main finding is that the probability…
We approach the development of models and control strategies of susceptible-infected-susceptible (SIS) epidemic processes from the perspective of marked temporal point processes and stochastic optimal control of stochastic differential…
In this work, we derive a result of exponential stability for a coupled system of partial differential equations (PDEs) which governs a certain fluid-structure interaction. In particular, a three-dimensional Stokes flow interacts across a…
The critical properties displayed by an ideal 2D Bose gas trapped in a harmonic potential are determined and characterized in an exact numerical fashion. Beyond thermodynamics, addressed in terms of the global pressure and volume which are…
Differential balancing theory for nonlinear model reduction relies on differential controllability and observability functions. In this paper, we further investigate them from two different perspectives. First, we establish novel…
Entropic Outlier Sparsification (EOS) is proposed as a robust computational strategy for the detection of data anomalies in a broad class of learning methods, including the unsupervised problems (like detection of non-Gaussian outliers in…
Loss of trainability refers to a phenomenon in continual learning where parameter updates no longer make progress on the optimization objective, so accuracy stalls or degrades as the learning problem changes over time. In this paper, we…
Recently, Out-of-distribution (OOD) detection in dynamic graphs, which aims to identify whether incoming data deviates from the distribution of the in-distribution (ID) training set, has garnered considerable attention in security-sensitive…
We consider the neural ODE and optimal control perspective of supervised learning, with $\ell^1$-control penalties, where rather than only minimizing a final cost (the \emph{empirical risk}) for the state, we integrate this cost over the…
Neutron star observables like masses, radii, and tidal deformability are direct probes to the dense matter equation of state~(EoS). A novel deep learning method that optimizes an EoS in the automatic differentiation framework of solving…
We study a wave equation in one space dimension with a general diffusion coefficient which degenerates on part of the boundary. Degeneracy is measured by a real parameter $\mu_a>0$. We establish observability inequalities for weakly (when…
We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent…
A novel method of exponentially stable adaptive control to compensate for matched parametric uncertainty under a mild condition of semi-persistent excitation (s-PE) of a regressor with piecewise-constant rank and nullspace is proposed. It…
This paper deals with a class of neural SDEs and studies the limiting behavior of the associated sampled optimal control problems as the sample size grows to infinity. The neural SDEs with $N$ samples can be linked to the $N$-particle…
One of the most important questions nowadays in physics concerns the nature of the so-called dark energy. It is also a consensus among cosmologists that such a question will not be answered on the basis only of observational data. However,…
Exponential stability of the second order linear delay differential equation in $x$ and $u$-control $$ \ddot{x}(t)+a_1(t)\dot{x}(h_1(t))+a_2(t)x(h_2(t))+a_3(t)u(h_3(t))=0 $$ is studied, where indirect feedback control…
Exceptional points (EPs) represent non-Hermitian degeneracies where eigenvalues and eigenvectors coalesce, giving rise to enhanced sensitivity and critically damped dynamics. We demonstrate that when an EP coincides with a dissipative phase…
We consider the controllability problem for the continuity equation, corresponding to neural ordinary differential equations (ODEs), which describes how a probability measure is pushedforward by the flow. We show that the controlled…
The security of control systems under sensor attacks is investigated. Redundant observability is introduced, explaining existing security notions including the security index, attack detectability, and observability under attacks.…