Related papers: PDGM: a Neural Network Approach to Solve Path-Depe…
In this research, we explore neural network-based methods for pricing multidimensional American put options under the BlackScholes and Heston model, extending up to five dimensions. We focus on two approaches: the Time Deep Gradient Flow…
Many scientific and industrial applications require solving Partial Differential Equations (PDEs) to describe the physical phenomena of interest. Some examples can be found in the fields of aerodynamics, astrodynamics, combustion and many…
Recently proposed numerical algorithms for solving high-dimensional nonlinear partial differential equations (PDEs) based on neural networks have shown their remarkable performance. We review some of them and study their convergence…
We propose a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension, by making an analogy between the BSDE and reinforcement learning with the…
Detection and modeling of change-points in time-series can be considerably challenging. In this paper we approach this problem by incorporating the class of Dynamic Generalized Linear Models (DGLM) into the well know class of Product…
The paper represents the method for construction of the families of particular solutions to some new classes of $(n+1)$ dimensional nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic…
This paper introduces a differential dynamic programming (DDP) based framework for polynomial trajectory generation for differentially flat systems. In particular, instead of using a linear equation with increasing size to represent…
We present Mechanistic PDE Networks -- a model for discovery of governing partial differential equations from data. Mechanistic PDE Networks represent spatiotemporal data as space-time dependent linear partial differential equations in…
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…
Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…
We propose and analyze an iterative high-order hybridized discontinuous Galerkin (iHDG) discretization for linear partial differential equations. We improve our previous work (SIAM J. Sci. Comput. Vol. 39, No. 5, pp. S782--S808) in several…
We propose a deep learning based discontinuous Galerkin method (D2GM) to solve hyperbolic equations with discontinuous solutions and random uncertainties. The main computational challenges for such problems include discontinuities of the…
Recent advances in deep learning makes solving parabolic partial differential equations (PDEs) in high dimensional spaces possible via forward-backward stochastic differential equation (FBSDE) formulations. The implementation of most…
In this paper we introduce a numerical method for nonlinear parabolic PDEs that combines operator splitting with deep learning. It divides the PDE approximation problem into a sequence of separate learning problems. Since the computational…
We construct a deep learning-based numerical algorithm to solve path-dependent partial differential equations arising in the context of rough volatility. Our approach is based on interpreting the PDE as a solution to an BSDE, building upon…
Symbolic regression (SR) is the process of discovering hidden relationships from data with mathematical expressions, which is considered an effective way to reach interpretable machine learning (ML). Genetic programming (GP) has been the…
Data-driven discovery of partial differential equations (PDEs) has achieved considerable development in recent years. Several aspects of problems have been resolved by sparse regression-based and neural network-based methods. However, the…
In this paper, we develop an adaptive multiresolution discontinuous Galerkin (DG) scheme for time-dependent transport equations in multi-dimensions. The method is constructed using multiwavlelets on tensorized nested grids. Adaptivity is…
Solving partial differential equations (PDEs) on complex domains can present significant computational challenges. The Diffuse Domain Method (DDM) is an alternative that reformulates the partial differential equations on a larger, simpler…
This work addresses the accurate and efficient simulation of physical phenomena governed by parametric Partial Differential Equations (PDEs) characterized by varying boundary conditions, where parametric instances modify not only the…