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On fast simulation of dynamical system with neural vector enhanced numerical solver.

ABSTRACT: The large-scale simulation of dynamical systems is critical in numerous scientific and engineering disciplines. However, traditional numerical solvers are limited by the choice of step sizes when estimating integration, resulting in a trade-off between accuracy and computational efficiency. To address this challenge, we introduce a deep learning-based corrector called Neural Vector (NeurVec), which can compensate for integration errors and enable larger time step sizes in simulations. Our extensive experiments on a variety of complex dynamical system benchmarks demonstrate that NeurVec exhibits remarkable generalization capability on a continuous phase space, even when trained using limited and discrete data. NeurVec significantly accelerates traditional solvers, achieving speeds tens to hundreds of times faster while maintaining high levels of accuracy and stability. Moreover, NeurVec's simple-yet-effective design, combined with its ease of implementation, has the potential to establish a new paradigm for fast-solving differential equations based on deep learning.

SUBMITTER: Huang Z

PROVIDER: S-EPMC10502038 | biostudies-literature | 2023 Sep

REPOSITORIES: biostudies-literature

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On fast simulation of dynamical system with neural vector enhanced numerical solver.

Huang Zhongzhan Z Liang Senwei S Zhang Hong H Yang Haizhao H Lin Liang L

Scientific reports 20230914 1

The large-scale simulation of dynamical systems is critical in numerous scientific and engineering disciplines. However, traditional numerical solvers are limited by the choice of step sizes when estimating integration, resulting in a trade-off between accuracy and computational efficiency. To address this challenge, we introduce a deep learning-based corrector called Neural Vector (NeurVec), which can compensate for integration errors and enable larger time step sizes in simulations. Our extens ...[more]

PMID: 37709820

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Project description:Infrared neural stimulation (INS) delivered via short pulse trains is an innovative tool that has potential for us use for studying brain function and circuitry, brain machine interface, and clinical use. The prevailing mechanism for INS involves the conversion of light energy into thermal transients, leading to neuronal membrane depolarization. Due to the potential risks of thermal damage, it is crucial to ensure that the resulting local temperature increases are within non-damaging limits for brain tissues. Previous studies have estimated damage thresholds using histological methods and have modeled thermal effects based on peripheral nerves. However, additional quantitative measurements and modeling studies are needed for the central nervous system. Here, we performed 7 T MRI thermometry on ex vivo rat brains following the delivery of infrared pulse trains at five different intensities from 0.1-1.0 J/cm2 (each pulse train 1,875 nm, 25 us/pulse, 200 Hz, 0.5 s duration, delivered through 200 µm fiber). Additionally, we utilized the General BioHeat Transfer Model (GBHTM) to simulate local temperature changes in perfused brain tissues while delivering these laser energies to tissue (with optical parameters of human skin) via three different sizes of optical fibers at five energy intensities. The simulation results clearly demonstrate that a 0.5 second INS pulse train induces an increase followed by an immediate drop in temperature at stimulation offset. The delivery of multiple pulse trains with 2.5 s interstimulus interval (ISI) leads to rising temperatures that plateau. Both thermometry and modeling results show that, using parameters that are commonly used in biological applications (200 µm diameter fiber, 0.1-1.0 J/cm2), the final temperature increase at the end of the 60 sec stimuli duration does not exceed 1°C with stimulation values of 0.1-0.5 J/cm2 and does not exceed 2°C with stimulation values of up to 1.0 J/cm2. Thus, the maximum temperature rise is consistent with the thermal damage threshold reported in previous studies. This study provides a quantitative evaluation of the temperature changes induced by INS, suggesting that existing practices pose minimal major safety concerns for biological tissues.

Dataset Information

On fast simulation of dynamical system with neural vector enhanced numerical solver.

Publications

On fast simulation of dynamical system with neural vector enhanced numerical solver.

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