Results 1 to 10 of about 2,529,562 (187)

Convergence proof for first-order position-based dynamics: An efficient scheme for inequality constrained ODEs [PDF]

arXiv.org, 2023
NVIDIA researchers have pioneered an explicit method, position-based dynamics (PBD), for simulating systems with contact forces, gaining widespread use in computer graphics and animation.
Steffen Plunder, Sara Merino Aceituno
semanticscholar   +1 more source

On backpropagating Hessians through ODEs [PDF]

arXiv.org, 2023
We discuss the problem of numerically backpropagating Hessians through ordinary differential equations (ODEs) in various contexts and elucidate how different approaches may be favourable in specific situations.
Axel Ciceri, T. Fischbacher
semanticscholar   +1 more source

Classical structural identifiability methodology applied to low-dimensional dynamic systems in receptor theory

Journal of Pharmacokinetics and Pharmacodynamics, 2023
Mathematical modelling has become a key tool in pharmacological analysis, towards understanding dynamics of cell signalling and quantifying ligand-receptor interactions.
C. White, V. Rottschäfer, L. Bridge
semanticscholar   +1 more source

Personalized Algorithm Generation: A Case Study in Learning ODE Integrators [PDF]

SIAM Journal on Scientific Computing, 2021
We study the learning of numerical algorithms for scientific computing, which combines mathematically driven, handcrafted design of general algorithm structure with a data-driven adaptation to specific classes of tasks.
Yue Guo, Felix Dietrich, Tom S. Bertalan, Danimir T. Doncevic, M. Dahmen, I. Kevrekidis, Qianxiao Li   +6 more
semanticscholar   +1 more source

Semi-Implicit Multistep Extrapolation ODE Solvers

Mathematics, 2020
Multistep methods for the numerical solution of ordinary differential equations are an important class of applied mathematical techniques. This paper is motivated by recently reported advances in semi-implicit numerical integration methods, multistep and
D. Butusov, A. Tutueva, Petr Fedoseev, Artem A. Terentev, A. Karimov   +4 more
semanticscholar   +1 more source

Symmetry gaps for higher order ordinary differential equations [PDF]

Journal of Mathematical Analysis and Applications 2022, 2021
The maximal contact symmetry dimensions for scalar ODEs of order $\ge 4$ and vector ODEs of order $\ge 3$ are well known. Using a Cartan-geometric approach, we determine for these ODEs the next largest realizable (submaximal) symmetry dimension. Moreover, finer curvature-constrained submaximal symmetry dimensions are also classified.
arxiv   +1 more source

DYNAMICS OF COOPERATIVE REACTIONS BASED ON CHEMICAL KINETICS WITH REACTION SPEED: A COMPARATIVE ANALYSIS WITH SINGULAR AND NONSINGULAR KERNELS

Fractals, 2021
Chemical processes are constantly occurring in all existing creatures, and most of them contain proteins that are enzymes and perform as catalysts. To understand the dynamics of such phenomena, mathematical modeling is a powerful tool of study.
Zubair Ahmad, F. Ali, Aisha M. Alqahtani, Naveed Khan, I. Khan   +4 more
semanticscholar   +1 more source

Physics-guided neural networks (PGNNs) to solve differential equations for spatial analysis

Bulletin of the Polish Academy of Sciences: Technical Sciences, 2023
. Numerous examples of physically unjustified neural networks, despite satisfactory performance, generate contradictions with logic and lead to many inaccuracies in the final applications. One of the methods to justify the typical black-box model already
K. B. O. K. Bartłomiej BORZYSZKOWSKI BORZYSZKOWSKI o, Jakub Damaszke Jakub Karol DAMASZKE DAMASZKE, Marcin Romankiewicz Marcin Jakub ROMANKIEWICZ ROMANKIEWICZ, Marcin Świniarski and Marek and Marek, Marek Moszyński Moszy ´NSKI ∗∗∗ Moszy ´NSKI ∗∗∗   +4 more
semanticscholar   +1 more source

A Survey on Continuous Time Computations [PDF]

, 2007
We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models.
A Ben-Hur, A Ben-Hur, A Ben-Hur, A Ben-Hur, A Kempe, A Rabinovich, A Turing, A Vergis, A. Church, APL Francisco, Asarin, B Trakhtenbrot, BJ Copeland, C Moore, C Moore, C Moore, C Moore, CE Shannon, CS Calude, D Dee, D Deutsch, D Graça, D Woods, DS Graça, DS Graça, E Asarin, E Asarin, E Asarin, E Post, EB Davies, G Etesi, G Lafferriere, G P ăun, H Abdi, HM Stoll, HT Siegelmann, HT Siegelmann, HT Siegelmann, I Artobolevskii, I Németi, J Earman, J Foy, J Mycka, J Mycka, J Mycka, J Mycka, J Šíma, J Šíma, JF Costa, JJ Hopfield, JJ Hopfield, JV Tucker, K Ruohonen, K Ruohonen, K Ruohonen, K Ruohonen, K Ruohonen, K Ruohonen, K Weihrauch, K-I Ko, K-I Ko, L Blum, L Faybusovich, L Faybusovich, L Lipshitz, LA Rubel, LA Rubel, LM Adleman, M Campagnolo, M Campagnolo, M Casey, M Casey, M Davis, M Gori, M Hogarth, M Hogarth, M Hoyrup, M Pour-El, MB Pour-El, MB Pour-El, MB Pour-El, MD Bowles, ML Campagnolo, ML Campagnolo, ML Hogarth, MO Rabin, MS Branicky, MS Branicky, N Müller, O Bournez, O Bournez, O Bournez, O Bournez, O Bournez, O. Finkel, P Bouyer, P Clote, P Collins, P Koiran, P Koiran, P Koiran, P Orponen, P Orponen, PW Shor, R Alur, R Alur, R Legenstein, RJ Lipton, RW Brockett, RW Brockett, S Aaronson, S Grigorieff, S Omohundro, S. C. Kleene, T Brihaye, T Brihaye, T Head, T Natschläger, TA Henzinger, TD Kieu, U Helmke, V Bush, VD Blondel, VD Blondel, W Maass, W Maass, W Maass, W Maass, W Maass, W Maass, W Maass, W Maass, W Maass, W Maass, W Maass, W Maass, W Maass, WD Smith, Šíma   +138 more
core   +5 more sources

Mathematical modeling of the spread of the coronavirus under strict social restrictions

Mathematical Methods in the Applied Sciences, EarlyView., 2021
We formulate a simple susceptible‐infectious‐recovery (SIR) model to describe the spread of the coronavirus under strict social restrictions. The transmission rate in this model is exponentially decreasing with time. We find a formula for basic reproduction function and estimate the maximum number of daily infected individuals.
Mo'tassem Al‐arydah, Hailay Berhe, Khalid Dib, Kalyanasundaram Madhu   +3 more
wiley   +1 more source