2025-10-02 –, Coffee room
Language: English
Model Discovery is a symbolic-numeric method that modifies the physical equations of a dynamic system in order to fit test or telemetry data. In this talk, we introduce the Model Discovery pipeline in the Julia product Dyad, which builds upon Universal Differential Equations and other SciML methods.
Dynamic model calibration to data is a challenging problem, sometimes due to the nonlinear and stiff nature of the dynamic problem, the number of parameters to calibrate, or the fact that model has too many simplifying assumptions. In the context of component-based dynamic models, where each component represents a physical object, different levels of fidelity are used to construct each component, which are then composed at the system level for calibration against data. So when model calibration fails, a concrete possibility is that the components themselves are low fidelity.
In this scenario, Model Discovery can be used to identify which components and equations to augment and the exact symbolic expressions to augment with. That is the subject of this talk. Concretely, model discovery consists of four steps:
1. universal differential equations, which augments the dynamics with a neural network and regresses against the parameter of the neural network. Our implementation of this builds upon ModelingToolkitNeuralNets.jl.
2. output masking, a heuristic which determines which equations are the most critical to change in order to fit the data.
3. sensitivity analysis, built upon using SciMLSensitivity.jl, which identifies the correspondingly significant variables which influence the corrections. The above two steps reduce the input and output dimensions of the neural network.
4. Symbolic regression, which builds upon SymbolicRegression.jl, which approximates the neural network with symbolic regression using important parameters and variables from the original model.
Finally, this talk will demonstrate the method on a practical example of a thermo-fluid system called a cargo box, which is a fundamental unit in the modeling of Refrigerated Transport Units.
Ranjan is a sales engineer at JuliaHub, where he works with JuliaHub's modeling and simulation customers. He has a PhD in Applied Mathematics from MIT.
