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We propose new machine learning schemes for solving high dimensional nonlinear partial differential equations (PDEs). Relying on the classical backward stochastic differential equation (BSDE) representation of PDEs, our algorithms estimate…

The inverse problem of supervised reconstruction of depth-variable (time-dependent) parameters in a neural ordinary differential equation (NODE) is considered, that means finding the weights of a residual network with time continuous…

Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…

Adaptive inference is an effective mechanism to achieve a dynamic tradeoff between accuracy and computational cost in deep networks. Existing works mainly exploit architecture redundancy in network depth or width. In this paper, we focus on…

Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such as Residual networks (ResNets). They provide parameter efficiency and automate the model selection…

Neural ordinary differential equations (neural ODEs) have emerged as a novel network architecture that bridges dynamical systems and deep learning. However, the gradient obtained with the continuous adjoint method in the vanilla neural ODE…

By interpreting the forward dynamics of the latent representation of neural networks as an ordinary differential equation, Neural Ordinary Differential Equation (Neural ODE) emerged as an effective framework for modeling a system dynamics…

The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…

Optimal experimental design is a well studied field in applied science and engineering. Techniques for estimating such a design are commonly used within the framework of parameter estimation. Nonetheless, in recent years parameter…

In this paper, we introduce Path Integral Networks (PI-Net), a recurrent network representation of the Path Integral optimal control algorithm. The network includes both system dynamics and cost models, used for optimal control based…

This work considers the problem of control and resource scheduling in networked systems. We present DIRA, a Deep reinforcement learning based Iterative Resource Allocation algorithm, which is scalable and control-aware. Our algorithm is…

We develop a numerical method to reconstruct systems of ordinary differential equations (ODEs) from time series data without {\it a priori} knowledge of the underlying ODEs using sparse basis learning and sparse function reconstruction. We…

Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…

We present the Deep Picard Iteration (DPI) method, a new deep learning approach for solving high-dimensional partial differential equations (PDEs). The core innovation of DPI lies in its use of Picard iteration to reformulate the typically…

Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…

Hyperspectral Image (HSI) classification is an important issue in remote sensing field with extensive applications in earth science. In recent years, a large number of deep learning-based HSI classification methods have been proposed.…

Accurate forecasting of energy demand and supply is critical for optimizing sustainable energy systems, yet it is challenged by the variability of renewable sources and dynamic consumption patterns. This paper introduces a neural framework…

We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a…

We propose a data-driven framework for learning reduced-order moment dynamics from PDE-governed systems using Neural ODEs. In contrast to derivative-based methods like SINDy, which necessitate densely sampled data and are sensitive to…

Genetic Algorithm (GA) has been used in this paper for a new Nyquist based sub-optimal model reduction and optimal time domain tuning of PID and fractional order (FO) PI{\lambda}D{\mu} controllers. Comparative studies show that the new…