Results 41 to 50 of about 35,012 (233)

Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking

, 2010
We have recently solved the inverse spectral problem for integrable PDEs in arbitrary dimensions arising as commutation of multidimensional vector fields depending on a spectral parameter $\lambda$.
Bogdanov L, Bogdanov L, Dunajski M, Dunajski M Tod K P, Guil F, Kadomtsev B B, Kodama Y, Konopelchenko B, Manakov S V, Manakov S V, Manakov S V, Manakov S V Santini P M, Neyzi F, P M Santini, S V Manakov, Takasaki K Takebe T, Takasaki K Takebe T, Timman R Oswatitsch K, Zakharov V E, Zakharov V E, Zakharov V E, Zobolotskaya E A   +21 more
core   +1 more source

The Numerical Solution of Singularly Perturbed Nonlinear Partial Differential Equations in Three Space Variables: The Adaptive Explicit Inverse Preconditioning Approach

Modelling and Simulation in Engineering, 2019
Critical comments on the complexity of computational systems and the basic singularly perturbed (SP) concepts are given. A class of several complex SP nonlinear elliptic equations arising in various branches of science, technology, and engineering is ...
Anastasia-Dimitra Lipitakis
doaj   +1 more source

Families of Orbits Produced by Three-Dimensional Central and Polynomial Potentials: An Application to the 3D Harmonic Oscillator

Axioms, 2023
We study three-dimensional potentials of the form V=U(xp+yp+zp), where U is an arbitrary function of C2-class, and p∈Z, which produces a preassigned two-parametric family of spatial regular orbits given in the solved form f(x,y,z) = c1, g(x,y,z) = c2 (c1,
Thomas Kotoulas
doaj   +1 more source

On the injectivity of the circular Radon transform arising in thermoacoustic tomography

, 2004
The circular Radon transform integrates a function over the set of all spheres with a given set of centers. The problem of injectivity of this transform (as well as inversion formulas, range descriptions, etc.) arises in many fields from approximation ...
Agranovsky M, Agranovsky M, Andersson L-E, Bers L, Courant R, Denisjuk A, Ehrenpreis L, Fawcett J A, Finch D, Flatto L, Gelfand I, Gelfand I, Gindikin S, Helgason S, Hörmander L, John F, Kruger R A, Kuchment P, Louis A K, Natterer F, Natterer F, Nilsson S, Norton S J, Norton S J, Palamodov V P, Patch S K, Quinto E T, Quinto E T, Spivak M, Xu Y, Ya V, Zobin N   +31 more
core   +2 more sources

External optimal control of fractional parabolic PDEs

, 2019
In this paper we introduce a new notion of optimal control, or source identification in inverse, problems with fractional parabolic PDEs as constraints. This new notion allows a source/control placement outside the domain where the PDE is fulfilled.
Antil, Harbir, Verma, Deepanshu, Warma, Mahamadi   +2 more
core   +1 more source

Neural network augmented inverse problems for PDEs

, 2017
In this paper we show how to augment classical methods for inverse problems with artificial neural networks. The neural network acts as a prior for the coefficient to be estimated from noisy data. Neural networks are global, smooth function approximators and as such they do not require explicit regularization of the error functional to recover smooth ...
Berg, Jens, Nyström, Kaj
openaire   +2 more sources

AutomataGPT: Transformer‐Based Forecasting and Ruleset Inference for Two‐Dimensional Cellular Automata

Advanced Science, EarlyView.
We introduce AutomataGPT, a generative pretrained transformer (GPT) trained on synthetic spatiotemporal data from 2D cellular automata to learn symbolic rules. Demonstrating strong performance on both forward and inverse tasks, AutomataGPT establishes a scalable, domain‐agnostic framework for interpretable modeling, paving the way for future ...
Jaime A. Berkovich, Noah S. David, Markus J. Buehler   +2 more
wiley   +1 more source

The Inverse Spectral Transform for the Dunajski hierarchy and some of its reductions, I: Cauchy problem and longtime behavior of solutions

, 2015
In this paper we apply the formal Inverse Spectral Transform for integrable dispersionless PDEs arising from the commutation condition of pairs of one-parameter families of vector fields, recently developed by S. V. Manakov and one of the authors, to one
Santini, P. M., Yi, G.
core   +1 more source

AI in chemical engineering: From promise to practice

AIChE Journal, EarlyView.
Abstract Artificial intelligence (AI) in chemical engineering has moved from promise to practice: physics‐aware (gray‐box) models are gaining traction, reinforcement learning complements model predictive control (MPC), and generative AI powers documentation, digitization, and safety workflows.
Jia Wei Chew, Ronnie Andersson, Thomas Bierweiler, Patrik Ryttestal, Torsten Wik   +4 more
wiley   +1 more source

On numerical simulation of liquid polymer moulding

Mathematical Modelling and Analysis, 2003
In this paper we consider numerical algorithms for solving the system of nonlinear PDEs, arising in modeling of liquid polymer injection. We investigate the particular case when a porous preform is located within the mould, so that the liquid polymer is ...
R. Čiegis, O. Iliev
doaj   +1 more source