Related papers: Adaptive Finite Element Simulation of the Time-dep…
We consider parametric estimation for a parabolic linear second order stochastic partial differential equation (SPDE) from high frequency data which are observed in time and space. By using thinned data obtained from the high frequency…
Solving analytically intractable partial differential equations (PDEs) that involve at least one variable defined on an unbounded domain arises in numerous physical applications. Accurately solving unbounded domain PDEs requires efficient…
The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product polynomial expansions with respect to the parametric…
Predicting nutrient transport and salinity distribution is crucial for mitigating climate-related threats to agromaritime systems. Traditional PDE-based models can capture the physics of nutrient dispersion, salinity and water quality.…
We present a new method to sample conditioned trajectories of a system evolving under Langevin dynamics, based on Brownian bridges. The trajectories are conditioned to end at a certain point (or in a certain region) in space. The bridge…
In Rajeev (2013), 'Translation invariant diffusion in the space of tempered distributions', it was shown that there is an one to one correspondence between solutions of a class of finite dimensional SDEs and solutions of a class of SPDEs in…
In this paper, some new results on time-varying missile against a stationary target using pure proportional navigation (PPN) are developed in the planar interception problem. First, the relative motion equation is established in arc-length…
We analyze stochastic partial differential equations (SPDEs) with quadratic nonlinearities close to a change of stability. To this aim we compute finite-time Lyapunov exponents (FTLEs), observing a change of sign based on the interplay…
The radiative transport equation accurately describes light transport in participating media such as biological tissues, though analytic solutions are known only for simple geometries. We present a pseudospectral technique to efficiently…
This paper extends the finite element network analysis (FENA) to include a dynamic time-transient formulation. FENA was initially formulated in the context of the linear static analysis of 1D and 2D elastic structures. By introducing the…
A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution domain. Making use of neural forms for time-dependent…
This work proposes an $r$-adaptive finite element method (FEM) using neural networks (NNs). The method employs the Ritz energy functional as the loss function, currently limiting its applicability to symmetric and coercive problems, such as…
Spatial structure can arise in spatial point process models via a range of mechanisms, including neighbour-dependent directionally biased movement. This spatial structure is neglected by mean-field models, but can have important effects on…
This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…
We introduce a novel method to handle the time dimension when Physics-Informed Neural Networks (PINNs) are used to solve time-dependent differential equations; our proposal focuses on how time sampling and weighting strategies affect…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
A finite element model and its equivalent electronic analogue circuit of hydraulic transmission lines have been developed. Basic equations are approximated to be a set of ordinary differential equations that can be represented in state…
Two finite element approximations of the Oldroyd-B model for dilute polymeric fluids are considered, in bounded 2- and 3-dimensional domains, under no flow boundary conditions. The pressure and the symmetric conformation tensor are…
This paper studies the performative prediction problem which optimizes a stochastic loss function with data distribution that depends on the decision variable. We consider a setting where the agent(s) provides samples adapted to the…
A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model…