Related papers: Unbiased deep solvers for linear parametric PDEs
Artificial Neural Networks were recently shown to be an efficient representation of highly-entangled many-body quantum states. In practical applications, neural-network states inherit numerical schemes used in Variational Monte Carlo, most…
This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…
In this paper, we study the error in first order Sobolev norm in the approximation of solutions to linear parabolic PDEs. We use a Monte Carlo Euler scheme obtained from combining the Feynman--Kac representation with a Euler discretization…
This study presents a deep reinforcement learning approach for global hedging of long-term financial derivatives. A similar setup as in Coleman et al. (2007) is considered with the risk management of lookback options embedded in guarantees…
Approximate inference in probabilistic graphical models (PGMs) can be grouped into deterministic methods and Monte-Carlo-based methods. The former can often provide accurate and rapid inferences, but are typically associated with biases…
Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods…
We propose algorithms for solving high-dimensional Partial Differential Equations (PDEs) that combine a probabilistic interpretation of PDEs, through Feynman-Kac representation, with sparse interpolation. Monte-Carlo methods and…
In this paper we establish a connection between non-convex optimization methods for training deep neural networks and nonlinear partial differential equations (PDEs). Relaxation techniques arising in statistical physics which have already…
Can Monte Carlo (MC) solvers be directly used in gradient-based methods for PDE-constrained optimization problems? In these problems, a gradient of the loss function is typically presented as a product of two PDE solutions, one for the…
A method to increase the precision of feedforward networks is proposed. It requires a prior knowledge of a target function derivatives of several orders and uses this information in gradient based training. Forward pass calculates not only…
Partial differential equations frequently appear in the natural sciences and related disciplines. Solving them is often challenging, particularly in high dimensions, due to the "curse of dimensionality". In this work, we explore the…
The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a…
Recent research has used deep learning to develop partial differential equation (PDE) models in science and engineering. The functional form of the PDE is determined by a neural network, and the neural network parameters are calibrated to…
Uncertainty quantification for deep learning is a challenging open problem. Bayesian statistics offer a mathematically grounded framework to reason about uncertainties; however, approximate posteriors for modern neural networks still…
A novel generative machine learning approach for the simulation of sequences of financial price data with drawdowns quantifiably close to empirical data is introduced. Applications such as pricing drawdown insurance options or developing…
Financial derivatives are contracts that can have a complex payoff dependent upon underlying benchmark assets. In this work, we present a quantum algorithm for the Monte Carlo pricing of financial derivatives. We show how the relevant…
A method for approximating sixth-order ordinary differential equations is proposed, which utilizes a deep learning feedforward artificial neural network, referred to as a neural solver. The efficacy of this unsupervised machine learning…
Recently, several deep learning (DL) methods for approximating high-dimensional partial differential equations (PDEs) have been proposed. The interest that these methods have generated in the literature is in large part due to simulations…
Iterative differential approximation methods that rely upon backpropagation have enabled the optimization of neural networks; however, at present, they remain computationally expensive, especially when training models at scale. In this…
Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…