Related papers: Virtual domain extension for imposing boundary con…
This paper presents a novel and direct approach to price boundary and final-value problems, corresponding to barrier options, using forward deep learning to solve forward-backward stochastic differential equations (FBSDEs). Barrier…
Broad learning system (BLS) has been proposed for a few years. It demonstrates an effective learning capability for many classification and regression problems. However, BLS and its improved versions are mainly used to deal with…
In this paper we develop a stochastic boundary conditions (SBC) for event-driven molecular dynamics simulations of a finite volume embedded within an infinite environment. In this method, we first collect the statistics of…
Current virtual reality systems are typically limited by performance/cost, usability (size), or a combination of both. By using a networked client/server environment, we have solved these limitations for the client. However, in doing so we…
We introduce a novel Multimodal Neural Operator (MNO) architecture designed to learn solution operators for multi-parameter nonlinear boundary value problems (BVPs). Traditional neural operators primarily map either the PDE coefficients or…
A Waveguide Port Boundary Condition (WPBC) based on the restriction of the approximation space is presented in the context of Finite Element Analysis. As well as reducing the computational domain in the same manner as the traditional WPBC,…
An approach is presented for implicit time integration in computations of red blood cell flow by a spectral boundary integral method. The flow of a red cell in ambient fluid is represented as a boundary integral equation (BIE), whose…
The global push to advance Carbon Capture and Sequestration initiatives and green energy solutions, such as geothermal, have thrust new demands upon the current state-of-the-art subsurface fluid simulators. The requirement to be able to…
Domain Randomization (DR) is commonly used for sim2real transfer of reinforcement learning (RL) policies in robotics. Most DR approaches require a simulator with a fixed set of tunable parameters from the start of the training, from which…
Climate change necessitates rapid expansion of renewable energy, with wind energy offering a scalable and low-impact solution. However, accurate prediction of wind loads and power generation remains challenging due to uncertainties in wind…
The ability to discover optimal behaviour from fixed data sets has the potential to transfer the successes of reinforcement learning (RL) to domains where data collection is acutely problematic. In this offline setting, a key challenge is…
Control barrier functions (CBFs) enable guaranteed safe multi-agent navigation in the continuous domain. The resulting navigation performance, however, is highly sensitive to the underlying hyperparameters. Traditional approaches consider…
Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems (IBVPs) with non-zero boundary data that lead to bounded solutions. The new boundary procedure is applied to nonlinear IBVPs in…
We present a constructive method to devise boundary conditions for solutions of second-order elliptic equations so that these solutions satisfy specific qualitative properties such as: (i) the norm of the gradient of one solution is bounded…
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier--Stokes equations. A semi-discrete entropy estimate for the entire…
Initial boundary value problems arise commonly in applications with engineering and natural systems governed by nonlinear partial differential equations (PDEs). Operator learning is an emerging field for solving these equations by using a…
Minimizing PDE-residual losses is a common strategy to promote physical consistency in neural operators. However, standard formulations often lack variational correctness, meaning that small residuals do not guarantee small solution errors…
We introduce an innovative numerical technique based on convex optimization to solve a range of infinite dimensional variational problems arising from the application of the background method to fluid flows. In contrast to most existing…
A novel hybrid deep neural network architecture is designed to capture the spatial-temporal features of unsteady flows around moving boundaries directly from high-dimensional unsteady flow fields data. The hybrid deep neural network is…