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The covering approximation space evolves in time due to the explosion of the information, and the characteristic matrixes of coverings viewed as an effective approach to approximating the concept should update with time for knowledge…
We discuss kinetic-based particle optimization methods and variable-sample strategies for problems where the cost function represents the expected value of a random mapping. Kinetic-based optimization methods rely on a consensus mechanism…
We present an approach to solving problems in micromechanics that is amenable to massively parallel calculations through the use of graphical processing units and other accelerators. The problems lead to nonlinear differential equations…
Ideally, the time that an incremental algorithm uses to process a change should be a function of the size of the change rather than, say, the size of the entire current input. Based on a formalization of ``the set of things changed'' by an…
Parameter fitting of data to a proposed equation almost always consider these parameters as independent variables. Here, the method proposed optimizes an arbitrary number of variables by the minimization of a function of a single variable.…
A statistical, path-dependent framework to describe time-dependent macroscopic theories using the Principle of Maximum Caliber is presented. By means of this procedure, it is possible to infer predictive non-equilibrium statistical…
While policy optimization algorithms have played an important role in recent empirical success of Reinforcement Learning (RL), the existing theoretical understanding of policy optimization remains rather limited -- they are either…
We employ a canonical variational framework for the predictive characterization of structural instabilities that develop during the diffusion-driven transient swelling of hydrogels under geometrical constraints. The variational formulation…
In this paper, we introduce and analyze a class of numerical schemes that demonstrate remarkable superiority in terms of efficiency, the preservation of positivity, energy stability, and high-order precision to solve the time-dependent…
Particle-optimization-based sampling (POS) is a recently developed effective sampling technique that interactively updates a set of particles. A representative algorithm is the Stein variational gradient descent (SVGD). We prove, under…
This paper presents an adaptive sampling algorithm tailored for the optimization of parametrized dynamical systems using projection-based model order reduction. Unlike classical sampling strategies, this framework does not aim for a small…
A recently proposed method for computer simulations in the isothermal-isobaric (NPT) ensemble, based on Langevin-type equations of motion for the particle coordinates and the ``piston'' degree of freedom, is re-derived by straightforward…
Classical optimization is a cornerstone of the success of variational quantum algorithms, which often require determining the derivatives of the cost function relative to variational parameters. The computation of the cost function and its…
Predictions of relative stabilities of (competing) molecular crystals are of great technological relevance, most notably for the pharmaceutical industry. However, they present a long-standing challenge for modeling, as often minuscule free…
The complex physics and numerous failure modes of structural impact creates challenges when designing for impact resistance. While simple geometries of layered material are conventional, advances in 3D printing and additive manufacturing…
We consider a multi-period stochastic control problem where the multivariate driving stochastic factor of the system has known marginal distributions but uncertain dependence structure. To solve the problem, we propose to implement the…
Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…
A variational model of pressure-dependent plasticity employing a time-incremental setting is introduced. A novel formulation of the dissipation potential allows one to construct the condensed energy in a variationally consistent manner. For…
We introduce an approach to inferring the causal architecture of stochastic dynamical systems that extends rate distortion theory to use causal shielding---a natural principle of learning. We study two distinct cases of causal inference:…
Interfractional geometric uncertainties can lead to deviations of the actual delivered dose from the prescribed dose distribution. To better handle these uncertainties during treatment, the authors propose a dynamic framework for robust…