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.
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.
This paper proposes an unsupervised learning method to solve heat equations on chips.
problem Critical need for solving heat transfer equations on chips for 5G and AI.
method Hybrid framework of Auto Encoder and Image Gradient for unsupervised learning.
result Framework can solve heat transfer problems with a single training process and predict unseen cases.
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.
Methane is considered being a good choice as a propellant for future reusable launch systems. However, the heat transfer prediction for supercritical methane flowing in cooling channels of a regeneratively cooled combustion chamber is challenging. Because accurate heat transfer predictions are essential to design relia…
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.
Estimates heat equation on shrinking Ricci solitons with uniform bounds.
problem Analyzing heat equation on shrinking Ricci solitons.
method Proved L2 estimate with time-dependent Gaussian weight. result Uniform bounds for heat equation along Ricci flow.
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.
Introduce a thermodynamically informed, temperature-transferable MLCG framework for proteins.
problem Temperature transferability of MLCG models for proteins.
method Explicit decomposition of CG potential into energetic and entropic components.
result Reproduces temperature-dependent quantities like heat capacity.
Proposes learning manifold implicitly via heat kernel.
problem Direct manifold learning methods lack flexibility for down-stream applications.
method Implicit manifold learning using heat kernel.
result Framework achieves state-of-the-art results for data generation and Bayesian inference.
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…
Physics-based framework improves building energy forecasting.
problem Lack of physical correspondence in machine learning models for building energy systems.
method Combines LTI SSMs with subspace-based domain adaptation (SDA).
result Physics-derived subspaces align with data-derived subspaces for better forecasting.
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.
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.
CTS machines improve screen development in printing industries, reducing costs and increasing profitability.
problem Inefficient screen development process in heat transfer printing and labeling.
method Implementation of CTS (computer-to-screen) technology for screen development.
result Reduction in material and operational costs, leading to profitability.
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…
A new method trains physics-constrained neural networks more efficiently.
problem Training machine learning tools with limited data and physical constraints.
method Dual-Dimer method for searching saddle points in nonconvex-nonconcave functions.
result The Dual-Dimer method improves training efficiency and convergence speed.
We compute explicitly, and without any extra regularity assumptions, the large time limit of the fibrewise heat operator for Bismut-Lott type superconnections in the L^2-setting. This is motivated by index theory on certain non-compact spaces (families of manifolds with cocompact group action) where the convergence of …
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 …
This paper discusses the existence of gradient estimates for second order hypoelliptic heat kernels on manifolds. It is now standard that such inequalities, in the elliptic case, are equivalent to a lower bound on the Ricci tensor of the Riemannian metric. For hypoelliptic operators, the associated "Ricci curvature" ta…
We show that in dimension 4 and above, the lifespan of Ricci flows depends on the relative smallness of the Ricci curvature compared to the Riemann curvature on the initial manifold. We can generalize this lifespan estimate to the local Ricci flow, using which we prove the short-time existence of Ricci flow solutions o…
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.
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…
Develops kernels for matchings, overcoming computational challenges.
problem Challenges in applying kernel methods to matchings due to their discrete, non-Euclidean nature.
method Characterizes stationary kernels, introduces heat and Matérn kernel families, and develops a sub-exponential algorithm for efficient evaluation.
result Establishes novel negative results and identifies an open problem in transferring the framework to trees.
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.
In this paper, we quantify the statistical coherence between financial time series by means of the Renyi entropy. With the help of Campbell's coding theorem we show that the Renyi entropy selectively emphasizes only certain sectors of the underlying empirical distribution while strongly suppressing others. This accentu…
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.
The paper compares heat kernels on manifolds with Robin boundary conditions.
problem Comparing heat kernels on manifolds with different boundary conditions.
method Proving comparison theorems for heat kernels on geodesic balls and minimal submanifolds.
result Eigenvalue comparison theorem for the first Robin eigenvalues on minimal submanifolds.
We give a short proof of a strong version of the short time asymptotic expansion of heat kernels associated to Laplace type operators acting on sections of vector bundles over compact Riemannian manifolds, including exponential decay of the difference of the approximate heat kernel and the true heat kernel. We use this…
Study on biharmonic map heat flow with monotonicity formula.
problem Properties of biharmonic heat kernel and extrinsic biharmonic map heat flow.
method Derived an entropy type quantity exhibiting monotonicity behaviors.
result Monotonicity formula for extrinsic biharmonic map heat flow.
Study on uniquely determining thermal properties from boundary temperature and heat flux measurements.
problem Determine thermal conductivity and volumetric heat capacity from boundary measurements.
method Uniqueness proof for isotropic and anisotropic media under thermal diffusivity assumption.
result Uniqueness of thermal properties in all dimensions and up to a gauge in two dimensions.
Understanding the heat usage of customers is crucial for effective district heating operations and management. Unfortunately, existing knowledge about customers and their heat load behaviors is quite scarce. Most previous studies are limited to small-scale analyses that are not representative enough to understand the b…
We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We show explicitly that the obtaine…
The heat kernel for the Cauchy-Riemann subLaplacian on S(2n+1) is derived in a manner which is completely analogous to the classical derivation of elliptic heat kernels. This suggests that the classical hamiltonian construction of elliptic heat kernels, with appropriate modifications, does yield heat kernels for subell…
The paper studies heat kernel asymptotics and proves Morse inequalities.
problem Analyzing the asymptotic behavior of heat kernels near critical points.
method Localization and scaling techniques in semi-classical analysis.
result The heat kernel near critical points is approximated by harmonic oscillator kernels, leading to Morse inequalities.
Derives gradient estimates for CR heat equation on pseudo-Hermitian manifolds.
problem Estimating solutions to CR heat equation on complex manifolds.
method Local and global Li-Yau type gradient estimates.
result Gradient estimates and Harnack inequality for positive solutions.
New heat equation method solves intertwining problems in CR geometry.
problem Intertwining problems in conformal CR geometry.
method Heat equation and extension problems approach.
result New intertwining formulas derived.
The Liouville theorem is proven for V T-harmonic map heat flow.
problem Proving Liouville theorems for V T-harmonic maps.
method Analyzing heat flow on manifolds with specific properties.
result Liouville theorems established for V T-harmonic maps.
We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We argue that the obtained formal s…
New method predicts heat load in thermal grids using latent variables.
problem Predicting heat load in district energy systems.
method Combines nominal model for outdoor temperature with latent variable model for residual heat load.
result Proposed method achieves better prediction accuracy than artificial neural networks.
Paper studies heat flow for maps on manifolds, avoiding singularities.
problem Avoiding singularities in heat flow for maps on manifolds.
method Introduces regularized conformal heat flow for n-harmonic maps. result Regularized n-conformal heat flow does not develop finite time singularities. In this paper, we first give a direct proof for two recurrence relations of the heat kernels for hyperbolic spaces in \cite{DM}. Then, by similar computation, we give two similar recurrence relations of the heat kernels for spheres. Finally, as an application, we compute the diagonal of heat kernels for odd dimensional…
Formulae connect heat kernels on glued manifolds.
problem Connecting heat kernels on joined manifolds.
method Proved gluing formulae for Laplacian heat kernels.
result Formulae linking heat kernels on joined manifolds.
Proves upper bounds for heat kernels evolving on manifolds.
problem Bounding heat kernels on evolving manifolds.
method Logarithmic Sobolev inequalities and ultracontractivity estimates.
result Gaussian upper bounds for heat kernels are derived.