相关论文: Path-integral evolution of multivariate systems wi…

Advanced algorithms are necessary to obtain faster-than-real-time dynamic simulations in a number of different physical problems that are characterized by widely disparate time scales. Recent advanced dynamic Monte Carlo algorithms that…

This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…

We present a multilevel Monte Carlo (MLMC) method for the uncertainty quantification of variably saturated porous media flow that are modeled using the Richards' equation. We propose a stochastic extension for the empirical models that are…

One of the less well understood ambiguities of quantization is emphasized to result from the presence of higher-order time derivatives in the Lagrangians resulting in multiple-valued Hamiltonians. We explore certain classes of branched…

We show that Lasso and Bayesian Lasso are very close when the sparsity is large and the noise is small. Then we propose to solve Bayesian Lasso using multivalued stochastic differential equation. We obtain three discretizations algorithms,…

Integrated Gradients has become a popular method for post-hoc model interpretability. De-spite its popularity, the composition and relative impact of different regions of the integral path are not well understood. We explore these effects…

Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…

This work is devoted to deriving the Onsager--Machlup function for a class of degenerate stochastic dynamical systems with (non-Gaussian) L\'{e}vy noise as well as Brownian noise. This is obtained based on the Girsanov transformation and…

Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such…

We use a recently found method to characterise all the invertible fourth-order difference equations linear in the extremal values based on the existence of a discrete Lagrangian. We also give some result on the integrability properties of…

This work is devoted to convergence analysis of an exponential integrator scheme for semi-discretization in time of nonlinear stochastic wave equation. A unified framework is first set forth, which covers important cases of additive and…

We focus on estimating the integrated covariance of log-price processes in the presence of market microstructure noise. We construct an efficient unbiased estimator for the quadratic covariation of two It\^{o} processes in the case where…

The problem of Relativistic Oscillator has been studied in the framework of Path Integral Monte-Carlo(PIMC) approach. Ultra-relativistic and non-relativistic limits have been discussed. We show that PIMC method can be effectively used for…

We introduce a Monte-Carlo algorithm for the simulation of charged particles moving in the continuum. Electrostatic interactions are not instantaneous as in conventional approaches, but are mediated by a constrained, diffusing electric…

Semiclassical path integral expression for a quantum system coupled to a harmonic bath is derived based on the stationary phase condition. It is discovered that the system path is non-Markovian. Most strikingly, the system path not only…

On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.

An efficient technique is introduced for model inference of complex nonlinear dynamical systems driven by noise. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is…

There is strong evidence coming from Lorentzian dynamical triangulations that the unboundedness of the gravitational action is no obstacle to the construction of a well-defined non-perturbative path integral. In a continuum approach, a…

Correlation between microstructure noise and latent financial logarithmic returns is an empirically relevant phenomenon with sound theoretical justification. With few notable exceptions, all integrated variance estimators proposed in the…

In this paper, we propose a novel Gaussian process-based moving horizon estimation (MHE) framework for unknown nonlinear systems. On the one hand, we approximate the system dynamics by the posterior means of the learned Gaussian processes…