Related papers: Jacobian-free Efficient Pseudo-Likelihood (EPL) Al…

In recent years, implicit deep learning has emerged as a method to increase the effective depth of deep neural networks. While their training is memory-efficient, they are still significantly slower to train than their explicit…

Finding the optimal hyperparameters of a model can be cast as a bilevel optimization problem, typically solved using zero-order techniques. In this work we study first-order methods when the inner optimization problem is convex but…

In partial differential equations-based (PDE-based) inverse problems with many measurements, many large-scale discretized PDEs must be solved for each evaluation of the misfit or objective function. In the nonlinear case, evaluating the…

This paper presents a novel direct Jacobian total Lagrangian explicit dynamics (DJ-TLED) finite element algorithm for real-time nonlinear mechanics simulation. The nodal force contributions are expressed using only the Jacobian operator,…

Quasi-dynamic energy flow calculation is an indispensable tool for the heat and electricity integrated energy system (HE-IES) analysis. One solves the nonlinear partial differential algebraic equations to obtain thermal, hydraulic and…

Although current semi-supervised medical segmentation methods can achieve decent performance, they are still affected by the uncertainty in unlabeled data and model predictions, and there is currently a lack of effective strategies that can…

A survey on algorithms for computing discrete logarithms in Jacobians of curves over finite fields.

The solution of inverse problems in a variational setting finds best estimates of the model parameters by minimizing a cost function that penalizes the mismatch between model outputs and observations. The gradients required by the numerical…

We study the problem of optimal portfolio selection under stochastic volatility within a continuous time reinforcement learning framework with portfolio constraints. Exploration is modeled through entropy-regularized relaxed controls, where…

This article presents a Bayesian inferential method where the likelihood for a model is unknown but where data can easily be simulated from the model. We discretize simulated (continuous) data to estimate the implicit likelihood in a…

In this paper, a hybrid measurement- and model-based method is proposed which can estimate the dynamic state Jacobian matrix in near real-time. The proposed method is computationally efficient and robust to the variation of network…

We consider the probabilistic numerical scheme for fully nonlinear PDEs suggested in \cite{cstv}, and show that it can be introduced naturally as a combination of Monte Carlo and finite differences scheme without appealing to the theory of…

A new Jacobian approximation is developed for use in quasi-Newton methods for solving systems of nonlinear equations. The new hypersecant Jacobian approximation is intended for the special case where the evaluation of the functions whose…

Solving symmetric positive semidefinite linear systems is an essential task in many scientific computing problems. While Jacobi-type methods, including the classical Jacobi method and the weighted Jacobi method, exhibit simplicity in their…

We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…

The Scheduled Relaxation Jacobi (SRJ) method is a viable candidate as a high performance linear solver for elliptic partial differential equations (PDEs). The method greatly improves the convergence of the standard Jacobi iteration by…

In a previous work (Akian, Fodjo, 2016), we introduced a lower complexity probabilistic max-plus numerical method for solving fully nonlinear Hamilton-Jacobi-Bellman equations associated to diffusion control problems involving a finite…

We show that the algorithm for computing an element of the Clarke generalized Jacobian of a max-type function proposed by Zheng-da Huang and Guo-chun Ma can be extended to a much wider class of functions representable as a difference of…

Many optimization problems require balancing multiple conflicting objectives. As gradient descent is limited to single-objective optimization, we introduce its direct generalization: Jacobian descent (JD). This algorithm iteratively updates…

The problem of monotone missing data has been broadly studied during the last two decades and has many applications in different fields such as bioinformatics or statistics. Commonly used imputation techniques require multiple iterations…