Results 21 to 30 of about 2,924,633 (320)
Structural And Multidisciplinary Optimization, 2021 Nonlinear dynamic structural optimization is a real challenge, in particular for problems that require the use of explicit solvers, e.g., crash. Here, the number of design variables is typically very limited.
J. Triller +3 more
semanticscholar +1 more source
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators [PDF]
Nature Machine Intelligence, 2019 It is widely known that neural networks (NNs) are universal approximators of continuous functions. However, a less known but powerful result is that a NN with a single hidden layer can accurately approximate any nonlinear continuous operator.
Lu Lu +4 more
semanticscholar +1 more source
Controllability distributions and systems approximations: a geometric approach [PDF]
, 1992 Given a nonlinear system, a relation between controllability distributions defined for a nonlinear system and a Taylor series approximation of it is determined. Special attention is given to this relation at the equilibrium.
Nijmeijer, H., Ruiz, A.C.
core +7 more sources
A nonlinear quantum adiabatic approximation [PDF]
Nonlinearity, 2020 This paper is devoted to a generalisation of the quantum adiabatic theorem to a nonlinear setting. We consider a Hamiltonian operator which depends on the time variable and on a finite number of parameters and acts on a separable Hilbert space of which we select a fixed basis. We study an evolution equation in which this Hamiltonian acts on the unknown
Clotilde Fermanian-Kammerer, Alain Joye
openaire +5 more sources
Solving Chance-Constrained Problems via a Smooth Sample-Based Nonlinear Approximation [PDF]
SIAM Journal on Optimization, 2019 We introduce a new method for solving nonlinear continuous optimization problems with chance constraints. Our method is based on a reformulation of the probabilistic constraint as a quantile function.
Alejandra Pena-Ordieres +2 more
semanticscholar +1 more source
International Journal of Adaptive Control and Signal Processing, EarlyView., 2023 Summary In this contribution, we propose a detailed study of interpolation‐based data‐driven methods that are of relevance in the model reduction and also in the systems and control communities. The data are given by samples of the transfer function of the underlying (unknown) model, that is, we analyze frequency‐response data.
Quirin Aumann, Ion Victor Gosea
wiley +1 more source
Nonlinear Approximation with Redundant Dictionaries [PDF]
Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005., 2006 In this paper we study nonlinear approximation and data representation with redundant function dictionaries. In particular, approximation with redundant wavelet bi-frame systems is studied in detail. Several results for orthonormal wavelets are generalized to the redundant case. In general, for a wavelet bi-frame system the approximation properties are
Borup, Lasse +2 more
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Data‐driven performance metrics for neural network learning
International Journal of Adaptive Control and Signal Processing, EarlyView., 2023 Summary Effectiveness of data‐driven neural learning in terms of both local mimima trapping and convergence rate is addressed. Such issues are investigated in a case study involving the training of one‐hidden‐layer feedforward neural networks with the extended Kalman filter, which reduces the search for the optimal network parameters to a state ...
Angelo Alessandri +2 more
wiley +1 more source
Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations [PDF]
Journal of nonlinear science, 2017 High-dimensional partial differential equations (PDEs) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment models, or portfolio optimization models. The PDEs in such applications are
C. Beck, Weinan E, Arnulf Jentzen
semanticscholar +1 more source
Numerical approximation of nonlinear SPDE’s
Stochastics and Partial Differential Equations: Analysis and Computations, 2022 AbstractThe numerical analysis of stochastic parabolic partial differential equations of the form $$\begin{aligned} du + A(u)\, dt = f \,dt + g \, dW, \end{aligned}$$ d u
Martin Ondreját +2 more
openaire +3 more sources