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A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed BLUES (Beyond Linear Use of Equation Superposition) function…
Nonlinear acceleration algorithms improve the performance of iterative methods, such as gradient descent, using the information contained in past iterates. However, their efficiency is still not entirely understood even in the quadratic…
This paper explores artificial intelligence (AI) methods for the approximate compiling of unitaries, focusing on the use of fixed two-qubit gates and arbitrary single-qubit rotations typical in superconducting hardware. Our approach…
The augmented Lagrangian (AL) method provides a flexible and efficient framework for solving extended-space full-waveform inversion (FWI), a constrained nonlinear optimization problem whereby we seek model parameters and wavefields that…
Recent hardware acceleration advances have enabled powerful specialized accelerators for finite element computations, spiking neural network inference, and sparse tensor operations. However, existing approaches face fundamental limitations:…
This paper proposes an accelerated version of Feasible Sequential Linear Programming (FSLP): the AA($d$)-FSLP algorithm. FSLP preserves feasibility in all intermediate iterates by means of an iterative update strategy which is based on…
In this paper, a new data-adaptive method, called DAIS (Data Adaptive ISolation), is introduced for the estimation of the number and the location of change-points in a given data sequence. The proposed method can detect changes in various…
We consider an inertial primal-dual fixed point algorithm (IPDFP) to compute the minimizations of the following Problem (1.1). This is a full splitting approach, in the sense that the nonsmooth functions are processed individually via their…
Anomaly detection for cyber-physical systems (ADCPS) is crucial in identifying faults and potential attacks by analyzing the time series of sensor measurements and actuator states. However, current methods lack adaptation to data…
In this paper, we develop an adaptive finite element method for the nonlinear steady-state Poisson-Nernst-Planck equations, where the spatial adaptivity for geometrical singularities and boundary layer effects are mainly considered. As a…
In this paper, we consider the Anderson acceleration method for solving the contractive fixed point problem, which is nonsmooth in general. We define a class of smoothing functions for the original nonsmooth fixed point mapping, which can…
This work presents an adaptive superfast proximal augmented Lagrangian (AS-PAL) method for solving linearly-constrained smooth nonconvex composite optimization problems. Each iteration of AS-PAL inexactly solves a possibly nonconvex…
Historically speaking, it is hard to balance the global and local efficiency of second-order optimization algorithms. For instance, the classical Newton's method possesses excellent local convergence but lacks global guarantees, often…
Training of deep neural networks (DNNs) frequently involves optimizing several millions or even billions of parameters. Even with modern computing architectures, the computational expense of DNN training can inhibit, for instance, network…
In this paper, we study the efficient numerical integration of functions with sharp gradients and cusps. An adaptive integration algorithm is presented that systematically improves the accuracy of the integration of a set of functions. The…
It is well known that Newton's method can have trouble converging if the initial guess is too far from the solution. Such a problem particularly occurs when this method is used to solve nonlinear elliptic partial differential equations…
In this paper we propose a unified two-phase scheme for convex optimization to accelerate: (1) the adaptive cubic regularization methods with exact/inexact Hessian matrices, and (2) the adaptive gradient method, without any knowledge of the…
We address the problem of clustering a set of points in $\mathbb{R}^d$ with axis-parallel clusters. Previous exact approaches to this problem are mostly based on integer programming formulations and can only solve to optimality instances of…
We present a new adaptive particle-based data assimilation scheme for cryospheric applications that leverages promising developments in importance sampling. The proposed approach seeks to combine some of the advantages of two widely used…
Training - the optimisation of complex models - is traditionally performed through small, local, iterative updates [D. E. Rumelhart, G. E. Hinton, R. J. Williams, Nature 323, 533-536 (1986)]. Approximating solutions through truncated…