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WOMBAT v2.S: A Bayesian inversion framework for attributing global CO2 flux components from multiprocess data

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arXiv 2025年

作者： Jacobson, Josh Bertolacci, Michael Zammit-Mangion, Andrew Schuh, Andrew Cressie, Noel School of Mathematics and Applied Statistics University of Wollongong Australia School of Physics Mathematics and Computing University of Western Australia Australia Colorado State University United States Jet Propulsion Laboratory California Institute of Technology United States

Contributions from photosynthesis and other natural components of the carbon cycle present the largest uncertainties in our understanding of carbon dioxide (CO2) sources and sinks. While the global spatiotemporal distribution of the net flux (the sum of all contributions) can be inferred from atmospheric CO2 concentrations through flux inversion, attributing the net flux to its individual components remains challenging. The advent of solar-induced fluorescence (SIF) satellite observations provides an opportunity to isolate natural components by anchoring gross primary productivity (GPP), the photosynthetic component of the net flux. Here, we introduce a novel statistical flux-inversion framework that simultaneously assimilates observations of SIF and CO2 concentration, extending WOMBAT v2.0 (WOllongong Methodology for Bayesian Assimilation of Trace-gases, version 2.0) with a hierarchical model of spatiotemporal dependence between GPP and SIF processes. We call the new framework WOMBAT v2.S, and we apply it to SIF and CO2 data from NASA’s Orbiting Carbon Observatory-2 (OCO-2) satellite and other instruments to estimate natural fluxes over the globe during a recent six-year period. In a simulation experiment that matches OCO-2’s retrieval characteristics, the inclusion of SIF improves accuracy and uncertainty quantification of component flux estimates. Comparing estimates from WOMBAT v2.S, v2.0, and the independent FLUXCOM initiative, we observe that linking GPP to SIF has little effect on net flux, as expected, but leads to spatial redistribution and more realistic seasonal structure in natural flux components. © 2025, CC BY.

关键词： NASA

Macroscopic finite-difference scheme based on the mesoscopic regularized lattice-Boltzmann method

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Physical Review E 2024年第2期109卷 025301-025301页

作者： Xi Liu Ying Chen Zhenhua Chai Baochang Shi School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China

In this paper, we develop a macroscopic finite-difference scheme from the mesoscopic regularized lattice Boltzmann (RLB) method to solve the Navier-Stokes equations (NSEs) and convection-diffusion equation (CDE). Unlike the commonly used RLB method based on the evolution of a set of distribution functions, this macroscopic finite-difference scheme is constructed based on the hydrodynamic variables of NSEs (density, momentum, and strain rate tensor) or macroscopic variables of CDE (concentration and flux), and thus shares low memory requirement and high computational efficiency. Based on an accuracy analysis, it is shown that, the same as the mesoscopic RLB method, the macroscopic finite-difference scheme also has a second-order accuracy in space. In addition, we would like to point out that compared with the RLB method and its equivalent macroscopic numerical scheme, the present macroscopic finite-difference scheme is much simpler and more efficient since it is only a two-level system with macroscopic variables. Finally, we perform some simulations of several benchmark problems, and find that the numerical results are not only in agreement with analytical solutions, but also consistent with the theoretical analysis.

关键词： Complex fluids Lattice-Boltzmann methods Navier-Stokes equation

Auto-ejection of liquid from a nozzle

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Physical Review E 2024年第4期109卷 045302-045302页

作者： Fang Shan Zhenhua Chai Baochang Shi School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan 430074 China

Auto-ejection of liquid is an important process in engineering applications, and is also very complicated since it involves interface moving, deforming, and jet breaking up. In this work, a theoretical velocity of meniscus at nozzle exit is first derived, which can be used to analyze the critical condition for auto-ejection of liquid. Then a consistent and conservative axisymmetric lattice Boltzmann (LB) method is proposed to study the auto-ejection process of liquid jet from a nozzle. We test the LB model by conducting some simulations, and find that the numerical results agree well with the theoretical and experimental data. We further consider the effects of contraction ratio, length ratio, contact angle, and nozzle structure on the auto-ejection, and observe some distinct phenomena during the ejection process, including the deformation of meniscus, capillary necking, and droplet pinch off. Finally, the results reported in the present work may play an instructive role on the design of droplet ejectors and the understanding of jetting dynamics in microgravity environment.

关键词： Lattice-Boltzmann methods

Digital twinning of cardiac electrophysiology models from the surface ECG: A geodesic backpropagation approach

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arXiv 2023年

作者： Grandits, Thomas Verhülsdonk, Jan Haase, Gundolf Effland, Alexander Pezzuto, Simone Department of Mathematics and Scientific Computing University of Graz Austria Institute for Applied Mathematics University of Bonn Germany Laboratory of Mathematics for Biology and Medicine Department of Mathematics University of Trento Italy NAWI Graz University of Graz Austria

The eikonal equation has become an indispensable tool for modeling cardiac electrical activation accurately and efficiently. In principle, by matching clinically recorded and eikonal-based electrocardiograms (ECGs), it is possible to build patient-specific models of cardiac electrophysiology in a purely non-invasive manner. Nonetheless, the fitting procedure remains a challenging task. The present study introduces a novel method, Geodesic-BP, to solve the inverse eikonal problem. Geodesic-BP is well-suited for GPU-accelerated machine learning frameworks, allowing us to optimize the parameters of the eikonal equation to reproduce a given ECG. We show that Geodesic-BP can reconstruct a simulated cardiac activation with high accuracy in a synthetic test case, even in the presence of modeling inaccuracies. Furthermore, we apply our algorithm to a publicly available dataset of a biventricular rabbit model, with promising results. Given the future shift towards personalized medicine, Geodesic-BP has the potential to help in future functionalizations of cardiac models meeting clinical time constraints while maintaining the physiological accuracy of state-of-the-art cardiac models. Copyright © 2023, The Authors. All rights reserved.

关键词： Electrocardiograms

New Results on the Solution for a Class of Integral Boundary Value Condition of Delay Partial Differential Equations with Fuzzy Data 7

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New Results on the Solution for a Class of Integral Boundary...

7th International Conference on Optimization and Applications, ICOA 2021

作者： Amma, Bouchra Ben Melliani, Said Chadli, Lalla Saadia Sultan Moulay Slimane University Laboratory of Applied Mathematics and Scientific Computing Beni MellalB.P523 Morocco

ISBN: (纸本)9781665441032

This work is an attempt to treat delay partial differential equations with fuzzy data. The main idea is to prove some results on the existence and uniqueness of solutions of intuitionistic fuzzy delay partial functional differential equations with integral boundary conditions by using Banach fixed-point theorem in a new weighted metric space. © 2021 IEEE.

关键词： Boundary value problems

VITO: VISION TRANSFORMER-OPERATOR

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arXiv 2023年

作者： Ovadia, Oded Turkel, Eli Kahana, Adar Karniadakis, George Em Stinis, Panos Department of Applied Mathematics Tel Aviv University Tel Aviv Israel Division of Applied Mathematics Brown University ProvidenceRI United States Advanced Computing Mathematics and Data Division Pacific Northwest National Laboratory RichlandWA United States

We combine vision transformers with operator learning to solve diverse inverse problems described by partial differential equations (PDEs). Our approach, named ViTO, combines a U-Net based architecture with a vision transformer. We apply ViTO to solve inverse PDE problems of increasing complexity, namely for the wave equation, the Navier-Stokes equations and the Darcy equation. We focus on the more challenging case of super-resolution, where the input dataset for the inverse problem is at a significantly coarser resolution than the output. The results we obtain are comparable or exceed the leading operator network benchmarks in terms of accuracy. Furthermore, ViTO’s architecture has a small number of trainable parameters (less than 10% of the leading competitor), resulting in a performance speed-up of over 5x when averaged over the various test cases. © 2023, CC BY.

关键词： Inverse problems

Automated Inference of Domain Knowledge in Scientific Machine Learning 19thth

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Automated Inference of Domain Knowledge in Scientific Mach...

19th International Conference on Computer Aided Systems Theory, EUROCAST 2024

作者： Bachinger, Florian Haider, Christian Zenisek, Jan de França, Fabrício Olivetti Affenzeller, Michael Heuristic and Evolutionary Algorithms Laboratory University of Applied Sciences Upper Austria Hagenberg Austria Johannes Kepler University Linz Austria Institute for Symbolic Artificial Intelligence Johannes Kepler University Linz Austria Center for Mathematics Computing and Cognition Federal University of ABC Santo André Brazil

ISBN: (纸本)9783031829512

The integration of prior knowledge into the training of machine learning (ML) models can improve their inter- and extrapolation capabilities and increases the trust of domain experts in model predictions. Shape-constrained regression is one category of ML algorithms capable of integrating knowledge about the shape of the model. Such knowledge is represented by boundary information of partial derivatives of different orders. However, the translation or formulation of (intrinsic) domain expert knowledge into such constraints is challenging and requires experience. Sometimes, this knowledge may even be unavailable for certain domains. We propose an approach that can automatically infer such knowledge from observational data. We envision this approach as an additional tool in the data analysis toolbox that provides suggestions, which can be incorporated into the training of prediction models. In this work, we describe our approach for automated knowledge inference from data. Additionally, we show the applicability of our approach by testing it on synthetic data generated from a set of physics equations. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Inference engines

Polynomial-Time Preparation of Low-Temperature Gibbs States for 2D Toric Code

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arXiv 2024年

作者： Ding, Zhiyan Li, Bowen Lin, Lin Zhang, Ruizhe Department of Mathematics University of California Berkeley United States Department of Mathematics City University of Hong Kong Hong Kong Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory United States Simons Institute for the Theory of Computing United States

We propose a polynomial-time algorithm for preparing the Gibbs state of the two-dimensional toric code Hamiltonian at any temperature, starting from any initial condition, significantly improving upon prior estimates that suggested exponential scaling with inverse temperature. Our approach combines the Lindblad dynamics using a local Davies generator with simple global jump operators to enable efficient transitions between logical sectors. We also prove that the Lindblad dynamics with a digitally implemented low temperature local Davies generator is able to efficiently drive the quantum state towards the ground state manifold. Despite this progress, we explain why protecting quantum information in the 2D toric code with passive dynamics remains challenging. © 2024, CC BY.

关键词： Polynomial approximation

An explicit, energy-conserving particle-in-cell scheme

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arXiv 2024年

作者： Ricketson, Lee F. Hu, Jingwei Lawrence Livermore National Laboratory Center for Applied Scientific Computing 7000 East Avenue LivermoreCA94550 United States Department of Applied Mathematics University of Washington Box 353925 SeattleWA98195 United States

We present an explicit temporal discretization of particle-in-cell schemes for the Vlasov equation that results in exact energy conservation when combined with an appropriate spatial discretization. The scheme is inspired by a simple, second-order explicit scheme that conserves energy exactly in the Eulerian context. We show that direct translation to particle-in-cell does not result in strict conservation, but derive a simple correction based on an analytically solvable optimization problem that recovers conservation. While this optimization problem is not guaranteed to have a real solution for every particle, we provide a correction that makes imaginary values extremely rare and still admits O(10−12) fractional errors in energy for practical simulation parameters. We present the scheme in both electrostatic – where we use the Ampère formulation – and electromagnetic contexts. With an electromagnetic field solve, the field update is most naturally linearly implicit, but the more computationally intensive particle update remains fully explicit. We also show how the scheme can be extended to use the fully explicit leapfrog and pseudospectral analytic time-domain (PSATD) field solvers. The scheme is tested on standard kinetic plasma problems, confirming its conservation properties. © 2024, CC BY-NC-ND.

关键词： Vlasov equation