Search Results for author:
Found 21 papers, 2 papers with code
Weak Convergence Analysis of Online Neural Actor-Critic Algorithms
Then, using a Poisson equation, we prove that the fluctuations of the model updates around the limit distribution due to the randomly-arriving data samples vanish as the number of parameter updates $\rightarrow \infty$.
Kernel Limit of Recurrent Neural Networks Trained on Ergodic Data Sequences
Mathematical methods are developed to characterize the asymptotics of recurrent neural networks (RNN) as the number of hidden units, data samples in the sequence, hidden state updates, and training steps simultaneously grow to infinity.
Global Convergence of Deep Galerkin and PINNs Methods for Solving Partial Differential Equations
In this paper, we prove global convergence for one of the commonly-used deep learning algorithms for solving PDEs, the Deep Galerkin Method (DGM).
Dynamic Deep Learning LES Closures: Online Optimization With Embedded DNS
The deep learning closure model is dynamically trained during a large-eddy simulation (LES) calculation using embedded direct numerical simulation (DNS) data.
Deep Learning Closure Models for Large-Eddy Simulation of Flows around Bluff Bodies
A deep learning (DL) closure model for large-eddy simulation (LES) is developed and evaluated for incompressible flows around a rectangular cylinder at moderate Reynolds numbers.
A Forward Propagation Algorithm for Online Optimization of Nonlinear Stochastic Differential Equations
We then re-write the algorithm using the PDE solution, which allows us to characterize the parameter evolution around the direction of steepest descent.
Neural Q-learning for solving PDEs
We develop a new numerical method for solving elliptic-type PDEs by adapting the Q-learning algorithm in reinforcement learning.
Continuous-time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations
The gradient estimate is simultaneously updated using forward propagation of the SDE state derivatives, asymptotically converging to the direction of steepest descent.
PDE-constrained Models with Neural Network Terms: Optimization and Global Convergence
Recent research has used deep learning to develop partial differential equation (PDE) models in science and engineering.
Embedded training of neural-network sub-grid-scale turbulence models
The weights of a deep neural network model are optimized in conjunction with the governing flow equations to provide a model for sub-grid-scale stresses in a temporally developing plane turbulent jet at Reynolds number $Re_0=6\, 000$.
DPM: A deep learning PDE augmentation method (with application to large-eddy simulation)
A deep neural network is embedded in a partial differential equation (PDE) that expresses the known physics and learns to describe the corresponding unknown or unrepresented physics from the data.
Asymptotics of Reinforcement Learning with Neural Networks
In addition, we study the convergence of the limit differential equation to the stationary solution.
Scaling Limit of Neural Networks with the Xavier Initialization and Convergence to a Global Minimum
We analyze single-layer neural networks with the Xavier initialization in the asymptotic regime of large numbers of hidden units and large numbers of stochastic gradient descent training steps.
Mean Field Analysis of Deep Neural Networks
The limit procedure is valid for any number of hidden layers and it naturally also describes the limiting behavior of the training loss.
Mean Field Analysis of Neural Networks: A Central Limit Theorem
We rigorously prove a central limit theorem for neural network models with a single hidden layer.
Universal features of price formation in financial markets: perspectives from Deep Learning
The universal price formation model is shown to exhibit a remarkably stable out-of-sample prediction accuracy across time, for a wide range of stocks from different sectors.
Stochastic Gradient Descent in Continuous Time: A Central Limit Theorem
Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance.
DGM: A deep learning algorithm for solving partial differential equations
The algorithm is tested on a class of high-dimensional free boundary PDEs, which we are able to accurately solve in up to $200$ dimensions.
Stochastic Gradient Descent in Continuous Time
Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance.
Deep Learning for Limit Order Books
The spatial neural network outperforms other models such as the naive empirical model, logistic regression (with nonlinear features), and a standard neural network architecture.
