2024-07-10 –, While Loop (4.2)
PiecewiseInference.jl is a novel inverse modelling framework specifically designed for the inference of parameters in large, nonlinear differential equation using time series data. It is based on a segmentation method together with minibatching. We briefly discuss its building blocks and demonstrate its performance with large ecosystem models. PiecewiseInference.jl is a user-friendly package that significantly simplifies the inference of parameters in complex dynamical models.
The inference of parameters in large, nonlinear differential equation models using time series data poses significant challenges. Bayesian methods, that infer the full posterior probability distribution of the unknown parameters, are computationally expensive and particularly prone to the curse of dimensionality. Alternatively, local-search methods based on variational optimizers are efficient but tend to converge to local minima. Here, we introduce PiecewiseInference.jl, an inverse modelling framework specifically designed for the inference of parameters in large, nonlinear differential equation using time series data. PiecewiseInference.jl improves the convergence of local-search methods by implementing a segmentation method and parameter constraints, which are used in combination with minibatching. By partitioning time-series data into shorter segments, the framework effectively regularizes the loss function, mitigating issues arising from the nonlinearities. The implementation of parameter constraints ensures that both model parameters and initial conditions remain within scientifically and numerically valid ranges, a critical aspect for the successful application of variational optimizers in inverse modeling problems.
Furthermore, the use of minibatching in PiecewiseInference.jl mitigates overfitting while reducing memory pressure. We briefly discuss the building blocks of PiecewiseInference.jl and demonstrate its performance on simulated food-web dynamics of increasing complexity. PiecewiseInference.jl is a user-friendly package that significantly simplifies the inference of parameters in complex dynamical models. Its ability to integrate data into complex scientific models enables their systematic testing and continuous development, making it a valuable asset for modelers in various fields.
I’m Victor, a postdoctoral researcher in the Dynamic Macroecology Group at the Swiss Federal Institute for Forest, Snow & Landscape (WSL), Switzerland. My work is centered on developing innovative models and methods to better understand and forecast the dynamics of ecosystems and their response to disruptions. My focus lies at the interface between process-based modelling and machine learning. I am specifically interested in leveraging the extrapolation ability of mechanistic models with the flexibility of state-of-the-art data driven techniques.