A5036562548- Magnetic confinement fusion research
- Model Reduction and Neural Networks
- Neural Networks and Applications
- Fluid Dynamics and Turbulent Flows
- Navier-Stokes equation solutions
- Computational Fluid Dynamics and Aerodynamics
- Seismic Imaging and Inversion Techniques
- Ionosphere and magnetosphere dynamics
- Fusion materials and technologies
- Solar and Space Plasma Dynamics
- Particle accelerators and beam dynamics
- Superconducting Materials and Applications
- Reservoir Engineering and Simulation Methods
- Nuclear reactor physics and engineering
- Dust and Plasma Wave Phenomena
- Numerical methods in inverse problems
- Groundwater flow and contamination studies
- Control Systems and Identification
- Stability and Controllability of Differential Equations
- Cosmology and Gravitation Theories
- Numerical Methods and Algorithms
- Stochastic processes and financial applications
- Gas Dynamics and Kinetic Theory
- Gaussian Processes and Bayesian Inference
- Stellar, planetary, and galactic studies
California Institute of Technology
2023-2024
ETH Zurich
2015-2022
Royal Military Academy
2020
École Polytechnique Fédérale de Lausanne
2016-2019
Board of the Swiss Federal Institutes of Technology
2015
Abstract DeepONets have recently been proposed as a framework for learning nonlinear operators mapping between infinite-dimensional Banach spaces. We analyze and prove estimates on the resulting approximation generalization errors. In particular, we extend universal property of to include measurable mappings in non-compact By decomposition error into encoding, reconstruction errors, both lower upper bounds total error, relating it spectral decay properties covariance operators, associated...
We derive bounds on the error, in high-order Sobolev norms, incurred approximation of Sobolev-regular as well analytic functions by neural networks with hyperbolic tangent activation function. These provide explicit estimates error respect to size networks. show that tanh only two hidden layers suffice approximate at comparable or better rates than much deeper ReLU
For several reasons the challenge to keep loads first wall within engineering limits is substantially higher in DEMO compared ITER. Therefore pre-conceptual design development for that currently ongoing Europe needs be based on load estimates are derived employing most recent plasma edge physics knowledge.
Fourier neural operators (FNOs) have recently been proposed as an effective framework for learning that map between infinite-dimensional spaces. We prove FNOs are universal, in the sense they can approximate any continuous operator to desired accuracy. Moreover, we suggest a mechanism by which associated with PDEs efficiently. Explicit error bounds derived show size of FNO, approximating Darcy type elliptic PDE and incompressible Navier-Stokes equations fluid dynamics, only increases sub...
Neural operator architectures approximate operators between infinite-dimensional Banach spaces of functions. They are gaining increased attention in computational science and engineering, due to their potential both accelerate traditional numerical methods enable data-driven discovery. A popular variant neural is the Fourier (FNO). Previous analysis proving universal approximation theorems for FNOs resorts use an unbounded number modes limits basic form method problems with periodic...
Operator learning refers to the application of ideas from machine approximate (typically nonlinear) operators mapping between Banach spaces functions. Such often arise physical models expressed in terms partial differential equations (PDEs). In this context, such hold great potential as efficient surrogate complement traditional numerical methods many-query tasks. Being data-driven, they also enable model discovery when a mathematical description PDE is not available. This review focuses...
Abstract Smooth solutions of the forced incompressible Euler equations satisfy an energy balance, where rate-of-change in time kinetic equals work done by force per unit time. Interesting phenomena such as turbulence are closely linked with rough which may exhibit inviscid dissipation , or, other words, for balance does not hold. This article provides a characterization physically realizable weak equations, i.e. obtained limit vanishing viscosity. More precisely, we show that,...
It is well known that parallel magnetic field fluctuations are connected with finite plasma beta effects. can therefore be expected Reduced Models simplify or neglect the may not capture salient physics of all types pressure gradient driven instabilities. This particularly true in axisymmetric toroidal plasmas which MHD instabilities always associated toroidicty and coupling poloidal mode harmonics. contribution examines distinct role perturbations on short long wavelength instabilities,...
PCA-Net is a recently proposed neural operator architecture which combines principal component analysis (PCA) with networks to approximate operators between infinite-dimensional function spaces. The present work develops approximation theory for this approach, improving and significantly extending previous in direction: First, novel universal result derived, under minimal assumptions on the underlying data-generating distribution. Then, two potential obstacles efficient learning are...
Neural operator architectures employ neural networks to approximate operators mapping between Banach spaces of functions; they may be used accelerate model evaluations via emulation, or discover models from data. Consequently, the methodology has received increasing attention over recent years, giving rise rapidly growing field learning. The first contribution this paper is prove that for general classes which are characterized only by their $C^r$- Lipschitz-regularity, learning suffers a...
We combine the spectral (viscosity) method and ensemble averaging to propose an algorithm that computes admissible measure valued solutions of incompressible Euler equations. The resulting approximate young measures are proved converge (with increasing numerical resolution) a solution. present experiments demonstrating robustness efficiency proposed algorithm, as well appropriateness solution framework for Furthermore, we report extensive computational study two dimensional vortex sheet,...
Absorption of Ion-Cyclotron Range Frequencies (ICRF) waves at the fundamental resonance is an efficient source plasma heating and fast ion generation in tokamaks stellarators.This method planned to be exploited as a Wendelstein 7-X stellarator.The work presented here assesses possibility using newly developed three-ion species scheme [Y.O. Kazakov et al., Nucl.Fusion 55, 032001 (2015)] tokamak stellarator plasmas, which could offer capability generating more energetic ions than traditional...
Operator learning has emerged as a new paradigm for the data-driven approximation of nonlinear operators. Despite its empirical success, theoretical underpinnings governing conditions efficient operator remain incomplete. The present work develops theory to study data complexity learning, complementing existing research on parametric complexity. We investigate fundamental question: How many input/output samples are needed in achieve desired accuracy $\epsilon$? This question is addressed...
Three dimensional free boundary magnetohydrodynamic equilibria that recover saturated ideal kink/peeling structures are obtained numerically. Simulations model the JET tokamak at fixed with a large edge bootstrap current flattens q-profile near plasma demonstrate radial parallel density ribbon dominant m /n = 5/1 Fourier component MA develops into broadband spectrum when toroidal It is increased to 2.5 MA.
A kinetic-magnetohydrodynamic model with kinetic pressure closure is derived from a consistent guiding-centre framework. Higher-order (gyroviscous) corrections to the tensor are in complex geometry reduced equation. The proposed allows for flows of order thermal ion velocity, taking into account important centrifugal effects due E × B flow, as well diamagnetic associated finite Larmor radius both fluid inertia and long mean-free path contributions. Wave–particle interactions, such toroidal...
We prove the conservation of energy for weak and statistical solutions two-dimensional Euler equations, generated as strong (in an appropriate topology) limits underlying Navier–Stokes equations a Monte Carlo-spectral viscosity numerical approximation, respectively. characterize this in terms uniform decay so-called structure function, allowing us to extend existing results on conservation. Moreover, we present experiments with wide variety initial data validate our theory observe large...
We propose and study the framework of dissipative statistical solutions for incompressible Euler equations. Statistical are time-parameterized probability measures on space square-integrable functions, whose time-evolution is determined from underlying prove partial well-posedness results a Monte Carlo type algorithm, based spectral viscosity spatial discretizations, to approximate them. Under verifiable hypotheses computations, we that approximations converge solution in suitable topology....
Coupled oscillators are being increasingly used as the basis of machine learning (ML) architectures, for instance in sequence modeling, graph representation and physical neural networks that analog ML devices. We introduce an abstract class encompasses these architectures prove universal, i.e, they can approximate any continuous casual operator mapping between time-varying functions, to desired accuracy. This universality result provides theoretical justification use oscillator based...
An improved set of guiding-centre equations, expanded to one order higher in Larmor radius than usually written for codes, are derived curvilinear flux coordinates and implemented into the orbit following code VENUS-LEVIS. Aside from greatly improving correspondence between full particle trajectories, most important effect additional corrections is modify definition guiding-centre's parallel velocity via so-called Banos drift. The correct treatment push-forward with term leads an anisotropic...
Smooth solutions of the forced incompressible Euler equations satisfy an energy balance, where rate-of-change in time kinetic equals work done by force per unit time. Interesting phenomena such as turbulence are closely linked with rough which may exhibit {\it inviscid dissipation}, or, other words, for balance does not hold. This article provides a characterization physically realizable weak equations, i.e. obtained limit vanishing viscosity. More precisely, we show that, two-dimensional...