Analysis of Vlasov plasma dynamics using matched pair Lie-Poisson formulation.
problem Understanding the dynamics of Vlasov plasma and its kinetic moments.
method Hamiltonian (Lie-Poisson) analysis and matched pair decomposition.
result Observation of mutual interactions between subdynamics in Vlasov plasma.
Unified geometric formulation of Maxwell-Vlasov system using presymplectic and symmetry reduction.
problem Unified geometric formulation of Maxwell-Vlasov system.
method Skinner-Rusk formalism, presymplectic geometry, reduction by diffeomorphism group, affine Hamiltonian controls.
result Unified geometric structure unifying Lagrangian, Hamiltonian, gauge, reduction, and control-theoretic aspects.
Neural network factorization speeds up Vlasov equation simulations.
problem Accelerating simulations of collisionless plasma described by the Vlasov equation.
method Data-driven low-rank matrix factorization using convolutional neural networks.
result The method outperforms standard linear algebra at inference time.
The action principle by Low [Proc. R. Soc. Lond. A 248, 282--287] for the classic Vlasov-Maxwell system contains a mix of Eulerian and Lagrangian variables. This renders the Noether analysis of reparametrization symmetries inconvenient, especially since the well-known energy- and momentum-conservation laws for the syst…
In this paper we construct the differential equations of the stream lines that characterize plasma regarded as a non-isotropic medium geometrized by a jet rheonomic time-invariant Berwald-Moor metric. Section 1 contains historical notes regarding the Plasma Physics and its geometrical description. Section 2 analyzes th…
In this paper, using Riemann-Lagrange geometrical methods, we construct a geometrical model on 1-jet spaces for the study of multi-time relativistic magnetized non-viscous plasma, characterized by a given energy-stress-momentum distinguished (d-) tensor. In that arena, we give the conservation laws and the continuity e…
Deep learning compares turbulence models in plasma physics.
problem Predicting edge plasma turbulence in magnetic fusion reactors.
method Physics-informed deep learning framework for comparing two-fluid and gyrokinetic models.
result Good overall agreement between two-fluid theory and gyrokinetic models in turbulent field fluctuations.
Inhomogeneous plasmas filaments instabilities are investigated by using the techniques of classical differential geometry of curves where Frenet torsion and curvature describe completely the motion of curves. In our case the Frenet frame changes in time and also depends upon the other coordinates taking into account th…
Physics-informed ML models improve turbulence understanding in fusion plasmas.
problem Improving turbulence modeling in fusion plasma devices.
method Physics-informed deep learning framework constrained by PDEs.
result Direct quantitative comparisons of turbulent fields between theory and gyrokinetic models.
Neural surrogates speed up 5D gyrokinetic simulations of plasma turbulence.
problem Expensive numerical simulations of plasma turbulence hinder fusion reactor design.
method Trained a hierarchical vision transformer in 5D to predict plasma quantities faster.
result Neural surrogates predict plasma quantities two orders of magnitude faster than numerical codes.
Study predicts turbulent electric fields in fusion plasmas using deep learning.
problem Predicting turbulent electric fields in fusion plasmas.
method Physics-informed deep learning, drift-reduced Braginskii theory, experimental data.
result Neutrals broaden turbulent field amplitudes and increase shearing rates.
GyroSwin models plasma turbulence with neural nets, reducing costs and capturing neglected nonlinearities.
problem Understanding plasma turbulence in fusion reactors, which impairs confinement and limits reactor design.
method Introduces GyroSwin, a scalable 5D neural surrogate that approximates 5D nonlinear gyrokinetic simulations.
result GyroSwin outperforms reduced models in heat flux prediction and captures turbulent energy cascade.
The multi-scale, mutli-physics nature of fusion plasmas makes predicting plasma events challenging. Recent advances in deep convolutional neural network architectures (CNN) utilizing dilated convolutions enable accurate predictions on sequences which have long-range, multi-scale characteristics, such as the time-series…
Deep learning is having a profound impact in many fields, especially those that involve some form of image processing. Deep neural networks excel in turning an input image into a set of high-level features. On the other hand, tomography deals with the inverse problem of recreating an image from a number of projections.…
Plasma toroidal metric singularities in helical devices and tokamaks, giving rise to magnetic surfaces inside the plasma devices are investigated in two cases. In the first we consider the case of a rotational plasma on an helical device with circular cross-section and dissipation. In this case singularities are shown …
Predicting unscheduled breakdowns of plasma etching equipment can reduce maintenance costs and production losses in the semiconductor industry. However, plasma etching is a complex procedure and it is hard to capture all relevant equipment properties and behaviors in a single physical model. Machine learning offers an …
Study proves stability of big bang singularity in complex system.
problem Stability of Kasner solutions in Einstein-Maxwell-scalar field-Vlasov system.
method Detailed mathematical structures and new delicate arguments.
result Nonlinear stability with Kasner exponents in full strong sub-critical regime.
INNs improve acceptance rates in electron spectra analysis.
problem Analyzing electron spectra from near-critical laser-plasmas.
method Invertible Neural Networks (INNs) for forward and inverse modeling.
result INNs significantly increase acceptance rates up to a factor of 10.
The paper analyzes McKean-Vlasov equations with hitting times, proving global solvability.
problem Analyzing blow-ups in McKean-Vlasov equations involving hitting times.
method Connection to the supercooled Stefan problem, comparison principles, and new transform.
result Proves global solvability for McKean-Vlasov dynamics under certain conditions.
Proves existence and trapped surface formation for Einstein-Vlasov system without symmetry assumptions.
problem Formation of trapped surfaces in Einstein-Vlasov system without symmetry.
method Calibrated hierarchy of estimates, refined renormalization, strategic restriction of elliptic estimates, precise commutator calculus.
result First large-data, symmetry-free construction of dynamical black hole formation.
A fast method learns plasma collision kernels from simulations, improving kinetic models.
problem Improving kinetic models for plasma dynamics beyond the weakly coupled regime.
method Data-driven collisional operator, fast spectral separation method.
result Accurately captures plasma dynamics in moderately coupled regime.
Minkowski space is shown to be globally stable as a solution to the Einstein--Vlasov system in the case when all particles have zero mass. The proof proceeds by showing that the matter must be supported in the "wave zone", and then proving a small data semi-global existence result for the characteristic initial value p…
A new method solves complex control problems with random coefficients.
problem Solving LQ McKean-Vlasov control problems with random coefficients.
method Decomposes the problem into two decoupled stochastic optimal control problems.
result The sum of optimal controls of auxiliary problems equals the original problem's optimal control.
Neural nets improve plasma equilibrium modeling for NSTX-U.
problem Modeling plasma equilibrium and shape control for NSTX-U.
method Developed two neural networks: Eqnet and Pertnet.
result NNs offer faster and more flexible prediction of plasma scenarios.
Riemannian geometrical tools, such as Ricci collineations and Killing symmetries, so often used in Einstein general theory of gravitation are here applied to plasma physics to build magnetic surfaces from Einstein plasma metrics used in tokamak devices. It is shown that the Killing symmetries are constrains the Einstei…
In this thesis, we consider the suitability of using the charged cold fluid model in the description of ultra-relativistic beams. The method that we have used is the following. Firstly, the necessary notions of kinetic theory and differential geometry of second order differential equations are explained. Then an averag…
Existence of calibrated local stochastic volatility models proven for non-regular coefficients.
problem Existence of calibrated local stochastic volatility models in finance.
method Investigation of McKean--Vlasov equations with minimal continuity assumptions on coefficients, providing existence and propagation of chaos results.
result Existence of calibrated local stochastic volatility models for appropriate stochastic volatility parameters.
New theorem links symmetries to first integrals in plasma physics.
problem Understanding the relationship between symmetries and first integrals in divergence-free fields.
method Developed a Noether-type Theorem reformulation for three-dimensional divergence-free vector fields.
result Converse of the Noether-type Theorem holds on the toroidal region, proving the existence of flux coordinates.
Novel RKHS approach solves complex financial model equations.
problem Calibrating singular local stochastic volatility models.
method Reproducing Kernel Hilbert Space (RKHS) regularization.
result Regularized model is well-posed and replicates option prices.
The paper solves complex control problems using neural networks.
problem Solving McKean-Vlasov control problems.
method Mean-field neural networks and algorithms based on dynamic programming and stochastic maximum principle.
result Extensive numerical results show the accuracy of the proposed algorithms.
We extend a model of positive feedback and contagion in large mean-field systems, by introducing a common source of noise driven by Brownian motion. Although the driving dynamics are continuous, the positive feedback effect can lead to `blow-up' phenomena whereby solutions develop jump-discontinuities. Our main results…
This paper extends transfer operator theory to McKean-Vlasov equations.
problem Analyzing the behavior of complex dynamical systems using transfer operators.
method Extended dynamic mode decomposition and Galerkin projection.
result Finite-dimensional approximations of transfer operators computed.
Study on massless Vlasov equation on Reissner-Nordström spacetimes, showing decay rates and non-decay phenomena.
problem Analyzing decay and non-decay rates of solutions to the massless Vlasov equation on Reissner-Nordström spacetimes.
method Quantitative analysis of geodesic flow and comparison to wave equation instability results.
result Exponential decay rates in subextremal cases and polynomial rates in extremal cases, with non-decay of transversal derivatives in extremal cases.
The paper extends Vlasov kinetic theory to time-dependent dynamics using cosymplectic and cocontact manifolds.
problem Extending Vlasov kinetic theory to time-dependent dynamics.
method Introducing geometric kinetic theories within cosymplectic and cocontact manifolds.
result Alternative realizations of cosymplectic and cocontact kinetic theories linked via Poisson/momentum maps.
We characterize stationary solutions to McKean-Vlasov equations on the circle.
problem Stationary solutions of McKean-Vlasov equations on the circle.
method Exact equivalence to an infinite-dimensional quadratic system of equations over Fourier coefficients, leading to explicit characterization of stationary states.
result Analytic expressions for the emergence, form, and shape of bifurcations involving multiple Fourier modes, and connections with discontinuous phase transitions.
Future stability of FLRW solutions in expanding 3D space is shown for compact perturbations.
problem Future stability of expanding FLRW solutions with spatial topology R^3.
method Nonlinear stability analysis of spherically symmetric perturbations.
result Decay rates of energy momentum tensor components compared to Minkowski space.
Framework optimizes expensive manufacturing processes efficiently.
problem Optimizing input parameters for advanced manufacturing methods.
method Bayesian optimization with tailored acquisition function and parallel acquisition.
result Framework efficiently finds optimal parameters with minimal process cost.
The first step to realize automatic experimental data analysis for fusion plasma experiments is fitting noisy data of temperature and density spatial profiles, which are obtained routinely. However, it has been difficult to construct algorithms that fit all the data without over- and under-fitting. In this paper, we sh…
Paper studies particle method for LSV model calibration, proving convergence and error bounds.
problem Calibration of local-stochastic volatility models with open well-posedness question.
method Regularized Euler--Maruyama scheme for particle approximation of McKean--Vlasov dynamics.
result Strong convergence of the Euler--Maruyama scheme with rate 1/2 in step-size.
New method improves Euler approximation for local stochastic volatility models.
problem Well-posedness of Euler approximation for local stochastic volatility models.
method Start with a well-defined Euler approximation to the formal McKean-Vlasov equation, followed by a half-step scheme.
result Showed weak order one for the Euler discretization, plus error terms.
Plasma tomography consists in reconstructing the 2D radiation profile in a poloidal cross-section of a fusion device, based on line-integrated measurements along several lines of sight. The reconstruction process is computationally intensive and, in practice, only a few reconstructions are usually computed per pulse. I…
We derive a diffusion approximation for the kinetic Vlasov-Fokker-Planck equation in bounded spatial domains with specular reflection type boundary conditions. The method of proof involves the construction of a particular class of test functions to be chosen in the weak formulation of the kinetic model. This involves t…
New approach finds solutions to games with unbounded controls.
problem Existence of equilibrium in mean-field games with unbounded controls.
method Weak formulation and new existence/stability results for quadratic-growth generalized McKean-Vlasov BSDEs.
result Existence of equilibrium result for non-Markovian mean-field games with unbounded control space.
Physics-Informed Neural Networks (PINNs) benchmarked against clinical estimator and reveal parameter identifiability
problem Chemotherapy pharmacokinetics (PK) with tissue concentration not measured
method Physics-Informed Neural Networks (PINNs) benchmarked against clinical estimator and reveal parameter identifiability
result PINN recovers tissue concentration and identifies non-identifiable parameters
The paper proves extremal black holes form at a critical point of gravitational collapse.
problem Formation of extremal black holes in gravitational collapse.
method Constructing smooth families of spherically symmetric solutions to the Einstein-Maxwell-Vlasov system.
result Extremal Reissner-Nordström black holes form at the critical collapse threshold.
New model explains market dynamics with phase transitions and non-linear interactions.
problem Understanding complex multi-asset market dynamics with phase transitions.
method Developed a Multi-Asset Non-Equilibrium Skew (MANES) model based on Langevin dynamics and McKean-Vlasov equation.
result The model accurately predicts market returns and phase transitions in both benign and distressed markets.
Method proves connection stability of vector fields on noncompact manifolds.
problem Stability of vector fields on noncompact manifolds.
method Developed a method to prove connection stability, showing equivalence to structural stability on compact manifolds.
result Presented an example of a connection stable vector field on a noncompact manifold and showed that harmonic oscillator is not connection stable.
New bidirectional model predicts magnetohydrodynamics fields and estimates uncertainty.
problem Predicting multiple fields in magnetohydrodynamics with uncertainty.
method Bidirectional autoregressive latent diffusion approach.
result Model can estimate uncertainty without ground truth using self-supervised consistency.