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We present quantitative means for assessing the numerical accuracy of static magnetic field calculations in finite-element models. Our calculations use the three-dimensional Opera simulation software suite of Dassault Syst`emes. Our need to…
A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…
This paper proposes an efficient method for the simultaneous estimation of the state of a quantum system and the classical parameters that govern its evolution. This hybrid approach benefits from efficient numerical methods for the…
Memristor based neural networks have great potentials in on-chip neuromorphic computing systems due to the fast computation and low-energy consumption. However, the imprecise properties of existing memristor devices generally result in…
In this paper, we consider the numerical approximation of a general second order semilinear stochastic partial differential equation (SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the nonlinear…
In this paper, we consider the problem of steering a family of independent, structurally identical, finite-dimensional stochastic linear systems with variation in system parameters between initial and target states of interest by using an…
Tree-based models are used in many high-stakes application domains such as finance and medicine, where robustness and interpretability are of utmost importance. Yet, methods for improving and certifying their robustness are severely…
We revisit two basic Direct Simulation Monte Carlo Methods to model aggregation kinetics and extend them for aggregation processes with collisional fragmentation (shattering). We test the performance and accuracy of the extended methods and…
In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such…
Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively.…
We introduce a guided stochastic sampling method that augments sampling from diffusion models with physics-based guidance derived from partial differential equation (PDE) residuals and observational constraints, ensuring generated samples…
The motivation of this work is to improve the performance of standard stacking approaches or ensembles, which are composed of simple, heterogeneous base models, through the integration of the generation and selection stages for regression…
One bottleneck of quantum Monte Carlo (QMC) simulation of strongly correlated electron systems lies at the scaling relation of computational complexity with respect to the system sizes. For generic lattice models of interacting fermions,…
A method is described for the development of the one-loop effective action expansion as an asymptotic series in inverse powers of the fermion mass. The method is based on the Schwinger-DeWitt proper-time technique, which allows for loop…
We develop a probabilistic machine learning method, which formulates a class of stochastic neural networks by a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced under the stochastic…
Power system state estimation (PSSE) is commonly formulated as weighted least-square (WLS) algorithm and solved using iterative methods such as Gauss-Newton methods. However, iterative methods have become more sensitive to system operating…
Nonlinear stochastic differential equations (NSDEs) are a pillar of mathematical modeling for scientific and engineering applications. Accurate and efficient simulation of large-scale NSDEs is prohibitive on classical computers due to the…
In recent years we have witnessed a growing interest in various non-equilibrium systems described in terms of stochastic non-linear field theories. In some of those systems like the KPZ and related models, the interesting behavior is in the…
We discuss the sign problem arising in Monte Carlo simulations of frustrated quantum spin systems. We show that for a class of ``semi-frustrated'' systems (Heisenberg models with ferromagnetic couplings $J_z(r) < 0$ along the $z$-axis and…
The numerical simulation of dynamical phenomena in interacting quantum systems is a notoriously hard problem. Although a number of promising numerical methods exist, they often have limited applicability due to the growth of entanglement or…