Biological activities observed in living systems occur as the output of which nanometer-, submicrometer-, and micrometer-sized structures and tissues non-linearly and dynamically behave through chemical reaction networks, including the generation of ...
Neural networks : the official journal of the International Neural Network Society
39874823
In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality reduction problem...
Neural networks : the official journal of the International Neural Network Society
39862534
The Physics-informed Neural Network (PINN) has been a popular method for solving partial differential equations (PDEs) due to its flexibility. However, PINN still faces challenges in characterizing spatio-temporal correlations when solving parametric...
Conjugate Gradient (CG) methods are widely used for solving large-scale nonlinear systems of equations arising in various real-life applications due to their efficiency in employing vector operations. However, the global convergence analysis of CG me...
The nonlinear Telegraph equation appears in a variety of engineering and science problems. This paper presents a deep learning algorithm termed physics-informed neural networks to resolve a hyperbolic nonlinear telegraph equation with Dirichlet, Neum...
The dynamics of neuron populations commonly evolve on low-dimensional manifolds. Thus, we need methods that learn the dynamical processes over neural manifolds to infer interpretable and consistent latent representations. We introduce a representatio...
Neural networks : the official journal of the International Neural Network Society
39955957
For unknown nonlinear systems with state constraints, it is difficult to achieve the safe optimal control by using Q-learning methods based on traditional quadratic utility functions. To solve this problem, this article proposes an accelerated safe Q...
International journal of computer assisted radiology and surgery
39953355
PURPOSE: Statistical shape models (SSMs) are widely used for morphological assessment of anatomical structures. However, a key limitation is the need for a clear relationship between the model's shape coefficients and clinically relevant anatomical p...
Earthworm-like robots have excellent locomotion capability in confined environments. Central pattern generator (CPG) based controllers utilize the dynamics of coupled nonlinear oscillators to spontaneously generate actuation signals for all segments,...
Neural networks : the official journal of the International Neural Network Society
39908912
Artificial neural networks are receiving increasing attention from researchers. However, with the advent of big data era, artificial neural networks are limited by the Von Neumann architecture, making it difficult to make new breakthroughs in hardwar...