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arXiv 2020年

作者： Zhang, Tianhan Zhang, Yaoyu Weinan, E. Ju, Yiguang Department of Mechanical and Aerospace Engineering Princeton University PrincetonNJ08544 United States School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Qing Yuan Research Institute Shanghai Jiao Tong University Shanghai200240 China Department of Mathematics Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Developing efficient and accurate algorithms for chemistry integration is a challenging task due to its strong stiffness and high dimensionality. The current work presents a deep learning-based numerical method called DeepCombustion0.0 to solve stiff ordinary differential equation systems. The homogeneous autoignition of DME/air mixture, including 54 species, is adopted as an example to illustrate the validity and accuracy of the algorithm. The training and testing datasets cover a wide range of temperature, pressure, and mixture conditions between 750 – 1200 K, 30 – 50 atm, and equivalence ratio = 0.7 – 1.5. Both the first-stage low-temperature ignition (LTI) and the second-stage high-temperature ignition (HTI) are considered. The methodology highlights the importance of the adaptive data sampling techniques, power transform preprocessing, and binary deep neural network (DNN) design. By using the adaptive random samplings and appropriate power transforms, smooth submanifolds in the state vector phase space are observed, on which two three-layer DNNs can be appropriately trained. The neural networks are end-to-end, which predict temporal gradients of the state vectors directly. The results show that temporal evolutions predicted by DNN agree well with traditional numerical methods in all state vector dimensions, including temperature, pressure, and species concentrations. Besides, the ignition delay time differences are within 1%. At the same time, the CPU time is reduced by more than 20 times and 200 times compared with the HMTS and VODE method, respectively. The current work demonstrates the enormous potential of applying the deep learning algorithm in chemical kinetics and combustion modeling. © 2020, CC BY.

关键词： Numerical methods

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Deep neural network for Wannier function centers

arXiv

引用

arXiv 2019年

作者： Zhang, Linfeng Chen, Mohan Wu, Xifan Wang, Han Weinan, E. Car, Roberto Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States CAPT HEDPS College of Engineering Peking University Beijing100871 China Department of Physics Temple University PhiladelphiaPA19122 United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Beijing Institute of Big Data Research Beijing100871 China Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States

We introduce a deep neural network (DNN) model that assigns the position of the centers of the electronic charge in the snapshots of a molecular dynamics trajectory. The electronic centers are uniquely specified by the unitary transformation that maps the occupied eigenstates onto maximally localized Wannier functions. In combination with deep potential molecular dynamics, a DNN approach to model the atomic potential energy surface at the ab initio density functional level of theory, the scheme makes possible to predict the dielectric properties of insulators for samples and trajectories inaccessible to direct ab initio simulation, without loss of accuracy. As an example, we report calculations of the infrared absorption spectra of light and heavy water at a dispersion inclusive hybrid functional level of theory, finding good agreement with experiment. Extensions to other spectroscopies, like Raman and sum frequency generation, are discussed. Copyright © 2019, The Authors. All rights reserved.

关键词： Quantum chemistry

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CellBiAge: Improved single-cell age classification using data binarization

引用

Cell Reports 2023年第12期42卷 113500页

作者： Yu, Doudou Li, Manlin Linghu, Guanjie Hu, Yihuan Hajdarovic, Kaitlyn H. Wang, An Singh, Ritambhara Webb, Ashley E. Molecular Biology Cell Biology and Biochemistry Graduate Program Brown University Providence 02912 RI United States Data Science Institute Brown University Providence 02912 RI United States Neuroscience Graduate Program Brown University Providence 02912 RI United States Department of Applied Mathematics & Statistics Johns Hopkins University Baltimore 21218 MD United States Department of Computer Science Brown University Providence 02912 RI United States Center for Computational Molecular Biology Brown University Providence 02912 RI United States Department of Molecular Biology Cell Biology and Biochemistry Brown University Providence 02912 RI United States Center on the Biology of Aging Brown University Providence 02912 RI United States Carney Institute for Brain Science Brown University Providence 02912 RI United States Center for Translational Neuroscience Brown University Providence 02912 RI United States

Aging is a major risk factor for many diseases. Accurate methods for predicting age in specific cell types are essential to understand the heterogeneity of aging and to assess rejuvenation strategies. However, classifying organismal age at single-cell resolution using transcriptomics is challenging due to sparsity and noise. Here, we developed CellBiAge, a robust and easy-to-implement machine learning pipeline, to classify the age of single cells in the mouse brain using single-cell transcriptomics. We show that binarization of gene expression values for the top highly variable genes significantly improved test performance across different models, techniques, sexes, and brain regions, with potential age-related genes identified for model prediction. Additionally, we demonstrate CellBiAge's ability to capture exercise-induced rejuvenation in neural stem cells. This study provides a broadly applicable approach for robust classification of organismal age of single cells in the mouse brain, which may aid in understanding the aging process and evaluating rejuvenation methods. © 2023 The Authors

关键词： aging brain CP: Cell biology hypothalamus machine learning single-cell RNA-seq

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Overview of the Head and Neck Tumor Segmentation for Magnetic Resonance Guided Applications (HNTS-MRG) 2024 Challenge

arXiv

引用

arXiv 2024年

作者： Wahid, Kareem A. Dede, Cem El-Habashy, Dina M. Kamel, Serageldin Rooney, Michael K. Khamis, Yomna Abdelaal, Moamen R.A. Ahmed, Sara Corrigan, Kelsey L. Chang, Enoch Dudzinski, Stephanie O. Salzillo, Travis C. McDonald, Brigid A. Mulder, Samuel L. McCullum, Lucas Alakayleh, Qusai Sjogreen, Carlos He, Renjie Mohamed, Abdallah S.R. Lai, Stephen Y. Christodouleas, John P. Schaefer, Andrew J. Naser, Mohamed A. Fuller, Clifton D. Department of Radiation Oncology The University of Texas MD Anderson Cancer HoustonTX United States Department of Imaging Physics The University of Texas MD Anderson Cancer HoustonTX United States Transitional Year Program Corewell Health Wiliam Beaumont Royal OakMI United States Department of Radiation Oncology University of Maryland School of Medicine BaltimoreMD United States Department of Clinical Oncology and Nuclear Medicine Faculty of Medicine Alexandria University Alexandria Egypt UT MD Anderson Cancer Center UTHealth Houston Graduate School of Biomedical Sciences Houston United States Department of Radiation Oncology Baylor College of Medicine HoustonTX United States Department of Head and Neck Surgery The University of Texas MD Anderson Cancer HoustonTX United States Elekta AtlantaGA United States Department of Computational Applied Mathematics and Operations Research Rice University HoustonTX United States

Magnetic resonance (MR)-guided radiation therapy (RT) is enhancing head and neck cancer (HNC) treatment through superior soft tissue contrast and longitudinal imaging capabilities. However, manual tumor segmentation remains a significant challenge, spurring interest in artificial intelligence (AI)-driven automation. To accelerate innovation in this field, we present the Head and Neck Tumor Segmentation for MR-Guided Applications (HNTS-MRG) 2024 Challenge, a satellite event of the 27th International Conference on Medical Image Computing and Computer Assisted Intervention. This challenge addresses the scarcity of large, publicly available AI-ready adaptive RT datasets in HNC and explores the potential of incorporating multi-timepoint data to enhance RT auto-segmentation performance. Participants tackled two HNC segmentation tasks: automatic delineation of primary gross tumor volume (GTVp) and gross metastatic regional lymph nodes (GTVn) on pre-RT (Task 1) and mid-RT (Task 2) T2-weighted scans. The challenge provided 150 HNC cases for training and 50 for testing, hosted on *** using a Docker submission framework. In total, 19 independent teams from across the world qualified by submitting both their algorithms and corresponding papers, resulting in 18 submissions for Task 1 and 15 submissions for Task 2. Evaluation using the mean aggregated Dice Similarity Coefficient showed top-performing AI methods achieved scores of 0.825 in Task 1 and 0.733 in Task 2. These results surpassed clinician interobserver variability benchmarks, marking significant strides in automated tumor segmentation for MR-guided RT applications in HNC. © 2024, CC BY.

关键词： Magnetic resonance imaging

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Superposition and mimicking theorems for conditional McKean-Vlasov equations

arXiv

引用

arXiv 2020年

作者： Lacker, Daniel Shkolnikov, Mykhaylo Zhang, Jiacheng IEOR Department Columbia University New YorkNY10027 United States ORFE Department Bendheim Center for Finance Program in Applied & Computational Mathematics Princeton University PrincetonNJ08544 United States ORFE Department Princeton University PrincetonNJ08544 United States

We consider conditional McKean-Vlasov stochastic differential equations (SDEs), such as the ones arising in the large-system limit of mean field games and particle systems with mean field interactions when common noise is present. The conditional time-marginals of the solutions to these SDEs satisfy non-linear stochastic partial differential equations (SPDEs) of the second order, whereas the laws of the conditional time-marginals follow Fokker-Planck equations on the space of probability measures. We prove two superposition principles: The first establishes that any solution of the SPDE can be lifted to a solution of the conditional McKean-Vlasov SDE, and the second guarantees that any solution of the Fokker-Planck equation on the space of probability measures can be lifted to a solution of the SPDE. We use these results to obtain a mimicking theorem which shows that the conditional time-marginals of an Itô process can be emulated by those of a solution to a conditional McKean-Vlasov SDE with Markovian coefficients. This yields, in particular, a tool for converting open-loop controls into Markovian ones in the context of controlled McKean-Vlasov *** Codes 60H10, 60H15, 35Q84, 93E20 Copyright © 2020, The Authors. All rights reserved.

关键词： Fokker Planck equation

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Convergence acceleration of ensemble Kalman inversion in nonlinear settings

arXiv

引用

arXiv 2019年

作者： Chada, Neil K. Tong, Xin T. Applied Mathematics and Computational Science Program King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia Department of Mathematics National University of Singapore 119077 Singapore

Many data-science problems can be formulated as an inverse problem, where the parameters are estimated by minimizing a proper loss function. When complicated black-box models are involved, derivative-free optimization tools are often needed. The ensemble Kalman filter (EnKF) is a particle-based derivative-free Bayesian algorithm originally designed for data assimilation. Recently, it has been applied to inverse problems for computational efficiency. The resulting algorithm, known as ensemble Kalman inversion (EKI), involves running an ensemble of particles with EnKF update rules so they can converge to a minimizer. In this article, we investigate EKI convergence in general nonlinear settings. To improve convergence speed and stability, we consider applying EKI with non-constant step-sizes and covariance inflation. We prove that EKI can hit critical points with finite steps in non-convex settings. We further prove that EKI converges to the global minimizer polynomially fast if the loss function is strongly convex. We verify the analysis presented with numerical experiments on two inverse problems. Copyright © 2019, The Authors. All rights reserved.

关键词： Inverse problems

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A Mathematical Model for Linguistic Universals

arXiv

引用

arXiv 2019年

作者： Weinan, E. Zhou, Yajun Department of Mathematics & Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Beijing Institute of Big Data Research Beijing100871 China

Inspired by chemical kinetics and neurobiology, we propose a mathematical theory for pattern recurrence in text documents, applicable to a wide variety of languages. We present a Markov model at the discourse level for Steven Pinker’s "mentalese", or chains of mental states that transcend the spoken/written forms. Such (potentially) universal temporal structures of textual patterns lead us to a language-independent semantic representation, or a translationally-invariant word embedding, thereby forming the common ground for both comprehensibility within a given language and translatability between different languages. Applying our model to documents of moderate lengths, without relying on external knowledge bases, we reconcile Noam Chomsky’s "poverty of stimulus" paradox with statistical learning of natural languages. Copyright © 2019, The Authors. All rights reserved.

关键词： Markov processes

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Exponential acceleration of macroscopic quantum tunneling in a Floquet Ising model

arXiv

引用

arXiv 2023年

作者： Grattan, George Barton, Brandon A. Feeney, Sean Mossi, Gianni Patnaik, Pratik Sagal, Jacob C. Carr, Lincoln D. Oganesyan, Vadim Kapit, Eliot Quantum Engineering Program Colorado School of Mines 1523 Illinois St CO Golden80401 United States Department of Computer Science Colorado School of Mines 1500 Illinois St CO Golden80401 United States Department of Applied Mathematics and Statistics Colorado School of Mines 1500 Illinois St CO Golden80401 United States Department of Physics Colorado School of Mines 1523 Illinois St CO Golden80401 United States KBR Inc. 601 Jefferson St. HoustonTX77002 United States NASA Ames Research Center Moffett FieldCA94035 United States Department of Physics and Astronomy College of Staten Island CUNY Staten IslandNY10314 United States Physics program and Initiative for the Theoretical Sciences The Graduate Center CUNY New YorkNY10016 United States Center for Computational Quantum Physics Flatiron Institute 162 5th Avenue New YorkNY10010 United States

The exponential suppression of macroscopic quantum tunneling (MQT) in the number of elements to be reconfigured is an essential element of broken symmetry phases. Slow MQT is also a core bottleneck in quantum algorithms, such as traversing an energy landscape in optimization, and adiabatic state preparation more generally. In this work, we demonstrate the possibility to accelerate MQT through Floquet engineering with the application of a uniform, high frequency transverse drive field. Using the ferromagnetic phase of the transverse field Ising model in one and two dimensions as a prototypical example, we identify three qualitatively distinct regimes as a function of drive strength: (i) for weak drive, the system exhibits exponentially slow MQT alongside robust magnetic order, as expected;(ii) at intermediate drive strength, we find polynomial decay of rates alongside vanishing magnetic order consistent with critical or paramagnetic state;(iii) at very strong drive strengths both the tunnelling rate and time-averaged magnetic order remain finite with increasing system size. We support these claims with extensive full wavefunction and matrix-product state numerical simulations, and theoretical analysis. An experimental test of these results presents a technologically important and novel scientific question accessible on NISQ-era quantum computers. © 2023, CC BY.

关键词： Ising model

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Reed-Muller Codes Polarize

Reed-Muller Codes Polarize

引用

Annual IEEE Symposium on Foundations of Computer Science

作者： Emmanuel Abbe Min Ye Mathematics Institute and the School of Computer and Communication Sciences at EPFL Switzerland Program in Applied and Computational Mathematics in Princeton University USA Department of Electrical Engineering Princeton University USA

Reed-Muller (RM) codes were introduced in 1954 and have long been conjectured to achieve Shannon's capacity on symmetric channels. The activity on this conjecture has recently been revived with the emergence of polar codes. RM codes and polar codes are generated by the same matrix G_m= [1/1 0/1] ^⊗m but using different subset of rows. RM codes select simply rows having largest weights. Polar codes select instead rows having the largest conditional mutual information proceeding top to down in G_m; while this is a more elaborate and channel-dependent rule, the top-to-down ordering allows Arikan to show that the conditional mutual information polarizes, and this gives directly a capacity-achieving code on any symmetric channel. RM codes are yet to be proved to have such a property, despite the recent success for the erasure channel. In this paper, we connect RM codes to polarization theory. We show that proceeding in the RM code ordering, i.e., not top-to-down but from the lightest to the heaviest rows in G_m, the conditional mutual information again polarizes. We further demonstrate that it does so faster than for polar codes. This implies that G_m contains another code, different than the polar code and called here the twin-RM code, that is provably capacity-achieving on any symmetric channel. This gives in particular a necessary condition for RM codes to achieve capacity on symmetric channels. It further gives a sufficient condition if the rows with largest conditional mutual information correspond to the heaviest rows, i.e., if the twin-RM code is the RM code. We demonstrate here that the two codes are at least similar and give further evidence that they are indeed the same.

关键词： Polar codes Mutual information Channel capacity Decoding Entropy Boolean functions

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The impact of cosmic ray feedback during the epoch of reionisation

arXiv

引用

arXiv 2025年

作者： Farcy, Marion Rosdahl, Joakim Dubois, Yohan Blaizot, Jérémy Martin-Alvarez, Sergio Haehnelt, Martin Kimm, Taysun Teyssier, Romain Institute for Physics Laboratory for Galaxy Evolution and Spectral Modelling EPFL Observatoire de Sauverny Chemin Pegasi 51 Versoix1290 Switzerland Centre de Recherche Astrophysique de Lyon CNRS UMR 5574 Univ. Lyon Ens de Lyon 9 avenue Charles André Saint-Genis-LavalF-69230 France Institut d’Astrophysique de Paris CNRS UMR 7095 Sorbonne Université 98 bis bd Arago Paris75014 France Stanford University StanfordCA94305 United States Kavli Institute for Cosmology Institute of Astronomy Madingley Road CambridgeCB3 0HA United Kingdom Department of Astronomy Yonsei University 50 Yonsei-ro Seodaemun-gu Seoul03722 Korea Republic of Department of Astrophysical Sciences Princeton University Peyton Hall PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University Fine Hall Washington Road PrincetonNJ08544-1000 United States

Galaxies form and evolve via a multitude of complex physics. In this work, we investigate the role of cosmic ray (CR) feedback in galaxy evolution and reionisation, by examining its impact on the escape of ionising radiation from galaxies. For this purpose, we present two sphinx cosmological radiation-magneto-hydrodynamics simulations, allowing for the first time a study of the impact of CR feedback on thousands of resolved galaxies during the Epoch of Reionisation (EoR). The simulations differ in their feedback prescriptions: one adopts a calibrated strong supernova (SN) feedback, while the other simulation reduces the strength of SN feedback and includes CR feedback instead. We show that both comparably regulate star formation, reasonably match observations of high-redshift UV luminosity functions, and produce a similar amount of hydrogen ionising photons. In contrast to the model with strong SN feedback, the model with CRs lead to incomplete reionisation, which is in strong disagreement with observational estimates of the reionisation history. This is due to CR feedback shaping the ISM differently, filling with gas the low density cavities otherwise carved by SN explosions. As a result, this reduces the escape of ionising photons, at any halo mass, and primarily in the close vicinity of the stars. Our study indicates that CR feedback regulates galaxy growth during the EoR, but negatively affects reionisation, a tension which paves the way for further exploration and refinement of existing galaxy formation and feedback models. Such improvements are crucial in order to capture and understand the process of reionisation and the underlying evolution of galaxies through cosmic time. © 2025, CC BY.

关键词： Cosmic rays

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