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Mathematical models based on systems of ordinary differential equations (ODEs) are frequently applied in various scientific fields to assess hypotheses, estimate key model parameters, and generate predictions about the system's state. To support their application, we present a comprehensive, easy‐to‐use, and flexible MATLAB toolbox,QuantDiffForecast, and associated tutorial to estimate parameters and generate short‐term forecasts with quantified uncertainty from dynamical models based on systems of ODEs. We provide software (https://github.com/gchowell/paramEstimation_forecasting_ODEmodels/) and detailed guidance on estimating parameters and forecasting time‐series trajectories that are characterized using ODEs with quantified uncertainty through a parametric bootstrapping approach. It includes functions that allow the user to infer model parameters and assess forecasting performance for different ODE models specified by the user, using different estimation methods and error structures in the data. The tutorial is intended for a diverse audience, including students training in dynamic systems, and will be broadly applicable to estimate parameters and generate forecasts from models based on ODEs. The functions included in the toolbox are illustrated using epidemic models with varying levels of complexity applied to data from the 1918 influenza pandemic in San Francisco. A tutorial video that demonstrates the functionality of the toolbox is included.
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FMint: Bridging Human Designed and Data Pretrained Models for Differential Equation Foundation Model for Dynamical Simulation
Abstract The fast simulation of dynamical systems is a key challenge in many scientific and engineering applications, such as weather forecasting, disease control, and drug discovery. With the recent success of deep learning, there is increasing interest in using neural networks to solve differential equations in a data‐driven manner. However, existing methods are either limited to specific types of differential equations or require large amounts of data for training. This restricts their practicality in many real‐world applications, where data is often scarce or expensive to obtain. To address this, a novel multi‐modal foundation model, namedFMint(FoundationModel based onInitialization) is proposed, to bridge the gap between human‐designed and data‐driven models for the fast simulation of dynamical systems. Built on a decoder‐only transformer architecture with in‐context learning, FMint utilizes both numerical and textual data to learn a universal error correction scheme for dynamical systems, using prompted sequences of coarse solutions from traditional solvers. The model is pre‐trained on a corpus of 400K ordinary differential equations (ODEs), and extensive experiments are performed on challenging ODEs that exhibit chaotic behavior and of high dimensionality. The results demonstrate the effectiveness of the proposed model in terms of both accuracy and efficiency compared to classical numerical solvers, highlighting FMint's potential as a general‐purpose solver for dynamical systems. This approach achieves an accuracy improvement of 1 to 2 orders of magnitude over state‐of‐the‐art dynamical system simulators, and delivers a 5X speedup compared to traditional numerical algorithms. The code for FMint is available athttps://github.com/margotyjx/FMint.
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- PAR ID:
- 10640876
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Advanced Theory and Simulations
- Volume:
- 8
- Issue:
- 8
- ISSN:
- 2513-0390
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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