AI helps forecasters understand TC convective evolution before intensification.
problem Challenges in extracting scientific insights from complex TC data.
method Combining AI prediction algorithms and classical statistical inference.
result Identifies patterns in TC convective structure leading to intensification.
DiffObs predicts global precipitation with realistic wave modes and low frequency variations.
problem Predicting global precipitation evolution using satellite observations.
method Autoregressive generative diffusion model trained on satellite data.
result Model generates realistic wave modes and low frequency variations, validating its potential for climate prediction.
We study the limiting behaviour of the empirical measure of a system of diffusions interacting through their ranks when the number of diffusions tends to infinity. We prove that the limiting dynamics is given by a McKean-Vlasov evolution equation. Moreover, we show that in a wide range of cases the evolution of the cum…
POSL predicts dynamic convection volumes in hemodiafiltration patients.
problem Continuous, personalised predictions in personalised medicine.
method Adapted POSL to dynamically predict convection volumes using combinations of parametric regressions and machine learning.
result POSL outperformed candidate learners in predicting convection volumes with lower errors and better calibration.
Physics-informed model reduces RBC simulation costs.
problem Computational infeasibility of direct numerical simulations for turbulent systems.
method Combines CNN and recurrent architecture, penalized with PDEs, uses conformal prediction.
result Significant reduction in computational cost for long-term simulations.
Artificial neural networks estimate model parameters from observations, reducing model errors.
problem Estimating parameters of convection-permitting models from observations.
method Training Bayesian neural networks and point estimate neural networks on atmospheric state observations.
result Artificial neural networks can estimate model parameters and their statistics.
New method detects TC imagery patterns for rapid intensity change.
problem Detecting upcoming rapid intensity changes in TC satellite imagery.
method Nonparametric test of association between images and event labels using neural networks and bootstrap.
result Identifies archetypes of infrared imagery associated with elevated rapid intensification risk.
We consider generalized linear transient convection-diffusion problems for differential forms on bounded domains in Rn. These involve Lie derivatives with respect to a prescribed smooth vector field. We construct both new Eulerian and semi-Lagrangian approaches to the discretization of the Lie derivatives…
LGAC enhances heat transfer in turbulent boundary layers using slot jets.
problem Enhancing convective heat transfer in turbulent boundary layers.
method Artificial intelligence-based linear genetic algorithms control (LGAC) with slot jets.
result LGAC optimizes heat transfer and flow asymmetry in turbulent boundary layers.
LPINNs solve complex PDEs by reformulating PINNs on Lagrangian frame, reducing training complexity.
problem Complexity in training PINNs, especially for convection-diffusion equations.
method Propose LPINNs, a Lagrangian reformulation of PINNs, with two branches solving state variables and characteristics curves.
result Loss landscapes of LPINNs are less sensitive to problem complexity compared to traditional PINNs.
Physics-informed neural networks improve surrogate modeling of turbulent Rayleigh-Bénard convection.
problem Modeling turbulent Rayleigh-Bénard convection with high accuracy and efficiency.
method Physics-informed neural networks (PINNs) with novel padding and regularization techniques.
result Significantly improved predictive accuracy of surrogate models at high Rayleigh numbers Ra = 2 × 10^9.
Most transport theorems---that is, a formula for the rate of change of an integral in which both the integrand and domain of integration depend on time---involve domains that evolve according to a flow map. Such domains are said to be convecting. Here a transport theorem for nonconvecting domains evolving on an embedde…
Climate projections continue to be marred by large uncertainties, which originate in processes that need to be parameterized, such as clouds, convection, and ecosystems. But rapid progress is now within reach. New computational tools and methods from data assimilation and machine learning make it possible to integrate …
A new method combines classical and machine learning PDE solvers efficiently.
problem Combining classical and machine learning PDE solvers to reduce computational cost and improve accuracy.
method Proposes an approximate greedy router to select solvers at each iteration, mimicking a greedy approach.
result Consistently reduces final error and AUC of the error trajectory compared to single-solver baselines and hybrid approaches.
A phase plot of the oil economy is built using the literature data of world oil production, price, and EROEI (Energy Returned on Energy Invested). An analogy between the oil economy and the Benard convection is proposed; some methods of interpretation and forecast of the system behavior are also shown based on "phase p…
DeepONets improve surrogate modeling for engineering systems.
problem Accurately modeling complex PDEs for engineering systems.
method DeepONets specialize in approximating mathematical operators for PDEs.
result DeepONets achieve high prediction accuracy and zero-shot capability.
We present a unified derivation of covariant time derivatives, which transform as tensors under a time-dependent coordinate change. Such derivatives are essential for formulating physical laws in a frame-independent manner. Three specific derivatives are described: convective, corotational, and directional. The covaria…
We propose a new high-order alternating direction implicit (ADI) finite difference scheme for the solution of initial-boundary value problems of convection-diffusion type with mixed derivatives and non-constant coefficients, as they arise from stochastic volatility models in option pricing. Our approach combines differ…
Defines observer-invariant time derivatives on moving surfaces.
problem Deriving appropriate definitions for time derivatives on surfaces that move.
method Systematically derived from spacetime settings, considering observer-invariance and covariance principles.
result Formulations applicable for computations of tangential n-tensor fields on moving surfaces.
Novel approach ensures stability of compact schemes for variable PDEs.
problem Ensuring stability of compact schemes for variable coefficient PDEs.
method Difference equation approach to derive stability conditions.
result Derives sufficient condition for unconditional stability.
The paper solves complex swing option pricing equations with numerical methods.
problem Valuation of swing options with jumps under a mean-reverting model.
method Proposes second-order numerical methods to solve PIDEs convection-dominated and with nonlocal integral terms.
result Numerical methods confirm second-order convergence behavior.
The paper explores how multiway data from PDEs can be accurately tracked using EnKF with specific covariance and precision estimators.
problem Tracking sparse and multiway structures in dynamical processes governed by PDEs.
method Examined several multiway covariance and precision matrix estimators in the context of physics-driven forecasting and EnKF.
result Multiway data from Poisson and convection-diffusion PDEs can be accurately tracked using EnKF with appropriate estimators.
The stability and robustness of compact schemes for parabolic PDEs are analyzed.
problem Stability and robustness of compact schemes for solving parabolic PDEs.
method Compact spatial discretization, Crank-Nicolson temporal discretization, eigenvalue analysis of amplification matrix.
result An upper bound on the condition number of the amplification matrix is derived, showing stability.
This paper deals with pricing of European and American options, when the underlying asset price follows Heston model, via the interior penalty discontinuous Galerkin finite element method (dGFEM). The advantages of dGFEM space discretization with Rannacher smoothing as time integrator with nonsmooth initial and boundar…
Climate projections suffer from uncertain equilibrium climate sensitivity. The reason behind this uncertainty is the resolution of global climate models, which is too coarse to resolve key processes such as clouds and convection. These processes are approximated using heuristics in a process called parameterization. Th…
The calculus correspondence has been known to exist between generic pedal evolutions and generic wave front evolutions. In this paper, we first extend the known results on the calculus correspondence to evolutions with multi-parameters, and then give applications of calculus correspondence. Moreover, we discuss the pos…
Study material evolution using groupoids to track intrinsic properties.
problem Tracking material evolution without considering the whole body.
method Construct a groupoid encoding intrinsic properties and characteristic foliations.
result Define the evolution equation for material points.
New analysis identifies key factors in wildfire-generated thunderstorms.
problem Understanding the causes of pyrocumulonimbus (pyroCb) storms.
method Invariant Causal Prediction, conditional independence test, greedy-ICP search algorithm.
result Identified seven causal predictors for pyroCb formation.
Recent work has shown deep learning can accelerate the prediction of physical dynamics relative to numerical solvers. However, limited physical accuracy and an inability to generalize under distributional shift limit its applicability to the real world. We propose to improve accuracy and generalization by incorporating…
The paper studies circular evolutes and involutes of framed curves in Euclidean space.
problem Investigating properties of framed curves and their evolutes and involutes.
method Definition and analysis of circular evolutes and involutes of framed curves, properties of normal surfaces, and their relations.
result Circular evolutes and involutes of framed curves are opposite operations under suitable assumptions, similar to fronts in the Euclidean plane.
The paper studies curve evolution using the PLR equation and its solutions.
problem Investigating the evolution of space curves governed by the PLR equation.
method Examined the Lund-Regge evolution and derived its representation in the Frenet frame, aligning with the Lax system of the PLR equation. Developed a construction method for curve families via the Sym formula.
result Described the Lund-Regge evolution corresponding to Date multi-soliton solutions to the PLR equation.
The paper defines evolutes and involutes for framed curves and their properties.
problem Defining evolutes and involutes for framed curves with singular points.
method Using the theory of framed curves and Bertrand type curves.
result Conditions for evolutes and involutes being inverse operations of framed curves.
Generative thermal design learns optimal shapes using multi-agent reinforcement learning.
problem Complex thermal design challenges due to convection-diffusion equation and boundary interactions.
method Cooperative multi-agent deep reinforcement learning with continuous geometric representation.
result Framework learns optimal design strategies without shape derivation or differentiable objectives.
Study the geometry and dynamics of skew evolutes and involutes, related to bicycle kinematics.
problem Understanding the geometry and dynamics of skew evolutes and involutes.
method Investigate the skew evolute and involute maps, comparing them to bicycle kinematics.
result The skew evolute and involute maps have properties analogous to bicycle kinematics.
The evolute of a smooth curve in an m-dimensional Euclidean space is the locus of centers of its osculating spheres, and the evolute of a spatial polygon is the polygon whose consecutive vertices are the centers of the spheres through the consecutive (m+1)-tuples of vertices of the original polygon. We study the iterat…
ccc-Autoevolutes are closed curves congruent to their evolutes, constructed via symmetry.
problem Constructing closed curves congruent to their evolutes.
method Modified Frenet equation, numerical solutions, symmetry.
result Found the smallest autoevolute as a trefoil knot.
Study evolutes of curves with varying smoothness.
problem Understanding evolutes of curves with low smoothness.
method Analyzing the relationship between curve smoothness and evolute regularity.
result Evolutes have one less order of smoothness than the parent curve in generic cases.
Current system thermal-hydraulic codes have limited credibility in simulating real plant conditions, especially when the geometry and boundary conditions are extrapolated beyond the range of test facilities. This paper proposes a data-driven approach, Feature Similarity Measurement FFSM), to establish a technical basis…
Defines horocyclic evolutes, parallels, and involutes of spacelike frontals in hyperbolic 2-space.
problem None explicitly stated; focuses on definitions and relations.
method Using enveloid theorem, defines horocyclic parallel and involute as normal envelopes of horocycles.
result Investigates relations among horocyclic evolutes, parallels, and involutes.
New boundary treatment improves accuracy for complex PDEs.
problem Order reduction in high-order IMEX schemes for multidimensional PDEs.
method Novel boundary treatment algorithms for Cartesian meshes, treating implicit-explicit stages similarly to interior points.
result Recovery of designed order of convergence by numerical verification.
This paper presents a model order reduction (MOR) approach for high dimensional problems in the analysis of financial risk. To understand the financial risks and possible outcomes, we have to perform several thousand simulations of the underlying product. These simulations are expensive and create a need for efficient …
Study on focal surfaces and evolutes of framed curves in hyperbolic 3-space using Legendrian duality.
problem Investigate differential geometry properties of framed curves, including singular points.
method Use Legendrian dualities to analyze focal surfaces and evolutes of hyperbolic framed curves.
result Show the relationship among focal surfaces, evolutes, and dual surfaces of evolutes.
Financial derivatives pricing aims to find the fair value of a financial contract on an underlying asset. Here we consider option pricing in the partial differential equations framework. The contemporary models lead to one-dimensional or multidimensional parabolic problems of the convection-diffusion type and generaliz…
Abstract In this paper, definition of involute-evolute curve couple in Galilean space is given and some well-known theorems for the involute-evolute curves are obtained in 3-dimensional Galilean space.
Paper presents a new approach to continuum mechanics using port-Hamiltonian framework.
problem Geometric formulation of solid and fluid mechanics.
method Port-Hamiltonian framework, Dirac structures, Hamiltonian reduction theory.
result Systematic derivation of port-Hamiltonian models for solid and fluid mechanics.
Geometric approach to Dirac operator evolution on spacetimes.
problem Constructing the Cauchy evolution operator for Lorentzian Dirac operators.
method Realizing the operator as a sum of oscillatory integrals, relating to Feynman propagator.
result Relating Cauchy evolution operators to Feynman propagators and constructing Hadamard states.
Geometrically reformulates elasticity theory using exterior calculus.
problem Formulating nonlinear elasticity theory geometrically.
method Using exterior calculus and bundle-valued differential forms.
result Equivalence to standard tensor calculus formulations.
Abstract reviews symmetry and reduction in dynamical systems.
problem Understanding symmetries and reductions in dynamical systems.
method Algebraic formulation for dynamics of physical systems.
result Describes a reduction procedure for classical and quantum evolutions.