DyCMaMod

DyCMaMod. Dinámica y control para el aprendizaje automático y la Modelización

Project reference. PID2023-146872OB-I00
Funded by: MINECO. Ministerio de Economía, Comercio y Empresa
Principal Investigator (PI): Prof. Enrique Zuazua, Prof. Rafael Orive
Host Institution: DeustoCCM, University of Deusto, Spain
Duration: 01.09.2024 – 31.08.2027

Goal

The DyCMaMod project (Dynamics and Control for Machine Learning and Modeling) develops new mathematical and computational foundations for scientific artificial intelligence by combining machine learning, control theory, partial differential equations (PDEs), and data-driven hybrid modeling. Its main objective is to design robust, interpretable, and efficient surrogate models capable of being integrated with mechanistic models inspired by physical principles.

The project has fosters new methodologies for the hybridization of data-driven models with continuous models governed by PDEs and kinetic equations, contributing to the development of hybrid frameworks capable of coherently and efficiently integrating experimental observations with physical knowledge. These research efforts open new perspectives for applications in fields such as biomedicine and healthy aging, scientific simulation, crowd dynamics, complex industrial systems, and the development of digital twins.

In this way, DyCMaMod therefore contributes directly to the thematic priority “Digital World, Industry, Space and Defence” through the development of new mathematical and computational technologies for advanced artificial intelligence, predictive modeling, distributed learning, and the simulation of complex systems. In addition, the project promotes knowledge transfer through collaborations with companies and technology centers, as well as through the development of an open GitHub-based platform for the dissemination of tools and scientific results.

Objectives

DyCMaMod focuses on integrating mechanical models with empirical data to create hybrid models.
This will be achieved through:
1. Generation of synthetic models using Neural Networks and reservoir computing to integrate real-time data.
2. Development of an innovative “collapse strategy” to minimize the discrepancy between synthetic and mechanical models.
3. Application of control techniques to adapt models to empirical data.
4. Use of methods based on particle dynamics, collective behavior, and kinetic equations.
5. Fusion of the “Random Batch Method” with Model PRedictive Control to reduce computational costs.
6. Creation of a computational platform with public access through DyCMaMod-GitHub.

Publications

DyCMaMod GitHub

• Decentralized Learning with coordination constraints
Author: Roberto Morales and Umberto Biccari
Language: Python
A source code to implement Decentralized Learning as a Multi-Objective Optimization problem.

• SHAP values for multi-output ML models
Author: Umberto Biccari, Roberto Morales and Enrique Zuazua
Language: Python
Computation of SHAP values for the interpretability of multi-output ML models.

• Riccati solution via DeepONet
Author: Jun Chen and Umberto Biccari
Language: Python
Training of Deep Operator Networks for the resolution of Algebraic and Differential Riccati equations.

• DeepONet for the stabilization of stochastic PDE-ODE systems
Author: Kaijing Lyu and Umberto Biccari
Language: Python
Training of Deep Operator Networks for the stabilization of stochastic PDE-ODE systems.

• DeepONet for the stabilization of reaction-diffusion systems
Author: Kaijing Lyu and Umberto Biccari
Language: Python
Training of Deep Operator Networks for the stabilization of reaction-diffusion systems.

• Semi-autonomous Neural ODEs to approximate dynamical systems
Author: Ziqian Li, Kang Liu, Lorenzo Liverani and Enrique Zuazua
Language: Python
A source code to approximate the behavior of dynamical systems using neural networks.

• Spiking Neural Networks
Author: Umberto Biccari
Language: Python
Code for training a basic Spiking Neural Network architecture.

• Fourier SHAP values
Author: Roberto Morales
Language: Python
Python implementation of Fourier-based SHAP values for explaining neural network predictions in a biomedical classification task.

• Sentiment analysis with transformers
Author: Albert Alcalde
Language: Python
An app for sentiment analysis using transformers.

• HYCO: The hybrid-collapse strategy for time-independent PDEs
Author: Lorenzo Liverani, Matthys Steynberg and Enrique Zuazua
Language: Python
Implementation of the HYCO strategy for the hybrid modelling of PDEs.

• Federated Learning: protect your data and privacy
Author: Ziqi Wang
Language: Python
A basic PyTorch implementation of the Federated Learning FedAvg algorithm.

• A potential game perspective in Federated Learning
Author: Kang Liu, Ziqi Wang and Enrique Zuazua
Language: Python
Implementation of a potential game strategy for Federated Learning

• FedADMM-InSa
Author: Yongcun Song, Ziqi Wang and Enrique Zuazua
Language: Python
Inexact and self-adaptive ADMM for Federated Learning.

• The ADMM-PINNs algorithmic framework for nonsmooth PDE-constrained optimization: A Deep Learning Approach
Author: Yongcun Song
Language: Python / MATLAB
A source code to study the combination of the alternating direction method of multipliers (ADMM) with physics-informed neural networks (PINNs) for a general class of nonsmooth partial differential equation (PDE)-constrained optimization problems, where additional regularization can be employed for constraints on the control or design variables.

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