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There are numerous advantages of deep neural network surrogate modeling for response time-history prediction. However, due to the high cost of refined numerical simulations and actual experiments, the lack of data has become an unavoidable…

Neural networks are powerful surrogates for numerous forward processes. The inversion of such surrogates is extremely valuable in science and engineering. The most important property of a successful neural inverse method is the performance…

We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an iterated rewriting system defines a formal class of models into which all the main architectures…

Can we evolve better training data for machine learning algorithms? To investigate this question we use population-based optimisation algorithms to generate artificial surrogate training data for naive Bayes for regression. We demonstrate…

Surrogates have been proposed as classical simulations of the pretrained quantum learning models, which are capable of mimicking the input-output relation inherent in the quantum model. Quantum hardware within this framework is used for…

Sequential prediction problems such as imitation learning, where future observations depend on previous predictions (actions), violate the common i.i.d. assumptions made in statistical learning. This leads to poor performance in theory and…

An extendable, efficient and explainable Machine Learning approach is proposed to represent cyclic plasticity and replace conventional material models based on the Radial Return Mapping algorithm. High accuracy and stability by means of a…

We propose a deep supervised learning algorithm based on low-discrepancy sequences as the training set. By a combination of theoretical arguments and extensive numerical experiments we demonstrate that the proposed algorithm significantly…

The development of data-informed predictive models for dynamical systems is of widespread interest in many disciplines. We present a unifying framework for blending mechanistic and machine-learning approaches to identify dynamical systems…

A supervised learning approach for the solution of large-scale nonlinear stabilization problems is presented. A stabilizing feedback law is trained from a dataset generated from State-dependent Riccati Equation solves. The training phase is…

Gradient-based algorithms for training ResNets typically require a forward pass of the input data, followed by back-propagating the objective gradient to update parameters, which are time-consuming for deep ResNets. To break the…

We present a simple linear regression based approach for learning the weights and biases of a neural network, as an alternative to standard gradient based backpropagation. The present work is exploratory in nature, and we restrict the…

In this work, we are concerned with neural network guided goal-oriented a posteriori error estimation and adaptivity using the dual weighted residual method. The primal problem is solved using classical Galerkin finite elements. The adjoint…

This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control…

The well-known generalization problem hinders the application of artificial neural networks in continuous-time prediction tasks with varying latent dynamics. In sharp contrast, biological systems can neatly adapt to evolving environments…

Transformers have demonstrated effectiveness in in-context solving data-fitting problems from various (latent) models, as reported by Garg et al. However, the absence of an inherent iterative structure in the transformer architecture…

This paper provides a preliminary study for an efficient learning algorithm by reasoning the error from first principle physics to generate learning signals in near real time. Motivated by iterative learning control (ILC), this learning…

Recently, Convolutional Neural Networks (CNNs) have shown promising performance in super-resolution (SR). However, these methods operate primarily on Low Resolution (LR) inputs for memory efficiency but this limits, as we demonstrate, their…

This article presents a new approach to the real-time solution of inverse problems on embedded systems. The class of problems addressed corresponds to ordinary differential equations (ODEs) with generalized linear constraints, whereby the…

A surrogate model that accurately predicts distribution system voltages is crucial for reliable smart grid planning and operation. This letter proposes a fixed-point data-driven surrogate modeling method that employs a limited dataset to…