Paper uses deep learning to improve thermal-hydraulic simulations.
problem Limited credibility of thermal-hydraulic codes in real plant conditions.
method Feature Similarity Measurement (FSM) and deep learning.
result Deep learning constructs relationships between local physical features and simulation errors.
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.
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…
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.
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.
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…
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.
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 …
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.
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.
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 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…
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.
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…
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…
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.
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.
In this paper we deal with two classes of mixed metric 3-structures, namely the mixed 3-Sasakian structures and the mixed metric 3-contact structures. Firstly we study some properties of the curvature of mixed 3-Sasakian structures, proving that any manifold endowed with such a structure is Einstein. Then we prove the …
Mixed-SCORE+ improves community detection in weak signal networks.
problem Detecting communities in weak signal networks.
method Proposes Mixed-SCORE+ combining properties of Mixed-SCORE and SCORE+.
result Significantly improves detection error rates on Polblogs and weak signal networks.
The paper explores knotoids, pseudo knotoids, braidoids, and pseudo braidoids on the torus.
problem The study of knotoids, pseudo knotoids, braidoids, and pseudo braidoids on the torus.
method Introducing new knotoid and braidoid concepts, isotopy theorems, state sum formulas, and Alexander and Markov theorems.
result Formulation and proof of Alexander and Markov theorems for mixed knotoids and mixed pseudo knotoids.
New method for mixed memberships using symmetrized Laplacian inverse matrix.
problem Mixed memberships in community detection.
method Spectral clustering on symmetrized Laplacian inverse matrix.
result Mixed-SLIM methods outperform state-of-the-art methods.
New mixed-platonic 3-manifolds from different polyhedra types.
problem Finding new hyperbolic knot complements with hidden symmetries.
method Defined mixed-platonic 3-manifolds and studied their properties.
result No mixed-platonic hyperbolic knot complement has hidden symmetries.
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.
The literature on statistical learning for time series assumes the asymptotic independence or ``mixing' of the data-generating process. These mixing assumptions are never tested, nor are there methods for estimating mixing rates from data. We give an estimator for the β-mixing rate based on a single stationary sample…
Unified Minkowski problem discussed for (p,q)-mixed quermassintegrals.
problem Unified Minkowski problem for (p,q)-mixed quermassintegrals.
method Introducing (p,q)-mixed quermassintegrals and (p,q)-dual mixed curvature measure to study the Minkowski problem.
result Derivation of important properties and geometric inequalities for (p,q)-mixed quermassintegrals.
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…
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.
Mix-IRLS solves imbalanced mixed linear regression problems efficiently.
problem Imbalanced mixed linear regression problems.
method Sequential robust regression approach.
result Mix-IRLS outperforms other methods on imbalanced mixtures and real-world datasets.
Mixed 3-structures are odd-dimensional analogues of paraquaternionic structures. They appear naturally on lightlike hypersurfaces of almost paraquaternionic hermitian manifolds. We study invariant and anti-invariant submanifolds in a manifold endowed with a mixed 3-structure and a compatible (semi-Riemannian) metric. P…
Paper presents an econophysics model for mixed economies.
problem Understanding mixed economies in various countries.
method Developed an econophysics model with a reduced state sector participation.
result Proposed a new model with a 10-15% state sector participation.
Proves almost flat manifolds with mixed curvature bounds.
problem Finding structures with mixed curvature bounds.
method Mixed curvature analogue of Gromov's almost flat manifolds theorem.
result Proves upper and lower curvature bounds for almost flat manifolds.
Characterizes measures preserving compound mixed renewal process properties.
problem Preserving compound mixed renewal process properties under different probability measures.
method Characterization of progressively equivalent probability measures.
result Any compound mixed renewal process can be converted into a compound mixed Poisson process through a change of measures.
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.
Improved deep dynamics models with symmetries for better accuracy and generalization.
problem Limited physical accuracy and inability to generalize under distributional shift in deep learning dynamics models.
method Incorporating symmetries into convolutional neural networks using various methods tailored to enforce different symmetries.
result Models robust to distributional shift by symmetry group transformations and favorable sample complexity.
Study on gradient descent in Hilbert spaces with Markov chains, focusing on mixing coefficients.
problem Analyzing convergence of gradient descent in Hilbert spaces with stationary Markov chains.
method Examined strictly stationary Markov chains with φ- and β-mixing coefficients, derived probabilistic upper bounds. result Probabilistic upper bounds on convergence behavior of gradient descent algorithm based on mixing coefficients.
Study on mixed Killing vector fields on Cigar Ricci-Bourguignon solitons.
problem Characterizing mixed Killing vector fields on Cigar Ricci-Bourguignon solitons.
method Analyzing the condition LVLVg=fLVg and using rigidity phenomena. result Dimension of complete mixed Killing fields is 5 and a basis is explicitly determined.
Study on Kähler manifolds with non-negative mixed curvature, proving splitting and structure theorems.
problem Investigating properties of Kähler manifolds with specific curvature conditions.
method Conformal perturbation method.
result Established structure and splitting theorems for Kähler manifolds with non-negative mixed curvature.