Franco-Indian call for proposals in Applied Mathematics and Artificial Intelligence

The objective of this Franco-Indian call is to promote value creation through research for the development of concepts and solutions in the fields corresponding to the following four thematic areas, as well as in sub-themes that may contribute to them.

1.    Mathematical Foundations of AI

Subtopics

• Geometric approaches and information geometry for AI: Geometric methods, including information geometry, offer insights into the structure and learning dynamics of AI models.
• Algebraic and formal modeling for AI, low rank matrix and tensor decomposition algebraic techniques provide tools for analyzing and designing AI models with structured representations. For example, deep convolution neural networks which are higher degree polynomial functions of inputs is a new class of neural networks which can be analyzed using algebraic techniques. 
• Stochastic modeling and AI and statistical evaluation (stochastic processes, random matrices, etc.). Stochastic models help capture randomness and uncertainty in AI systems, from training to prediction. Stochastic models and statistical evaluation will encompass stochastic approximation and Markov chain Monte Carlo methods with applications to machine learning, random matrices, queuing models and bandit optimization, among others. Non-uniform data across clients in federated learning is another paradigm.
• Analytical approaches: control-theoretic foundations of AI (stability properties, convergence behavior and guarantees), statistical learning theory, high-dimensional geometry and probability, as well as applications of approximation theory to machine learning.
• Limiting laws and guarantees for the behavior of large-scale AI systems.

2.    Theoretical foundations of Optimization and AI

Subtopics

• AI-assisted optimization and control: data-driven approaches. 
• Optimization in AI context: distributed data and models, concept drift/distributional shifts, multi-criteria optimization including regularization, optimization for non-Euclidean spaces.
• Fundamental limits of AI: complexity statements bounding the potential of generalization.
• Optimal transport theory: Optimal transport provides a powerful framework for comparing and aligning data distributions in AI.
• Automatic differentiation: approximating gradients and higher-order derivatives are a crucial component of efficient optimization techniques for machine learning, e.g., gradient-based methods are crucial for training deep learning models.
• Multi-agent environments: game theory, theory of cooperative reinforcement learning.

3.    Mathematics for safe, trustworthy and reliable AI

Subtopics

• Interpretability and explainability of AI systems are mandatory so that solutions provided by such systems can be explained (to humans), understood and accepted: formal methods and logical formalization, statistical theory of causality (in order to infer and leverage causal relations, rather than just correlations), representation and reasoning (creating mathematical models to improve reasoning capabilities of AI systems)
• Fairness to ensure the equity of the solutions provided by AI tools: optimal transport, sensitivity analysis, game theory, synthesis of fair-by-construction systems.
• Uncertainty quantifications in the context of AI solutions seek to ensure that AI systems perform reliably under perturbations or adversarial conditions, or with uncertain data: robustness aspects, propagation and retro-propagation, stochastic modeling, modal or interval logics.
• Frugality: Frugal AI emphasizes efficient learning using limited data, computation or energy resources: algorithms, optimization.

4.    AI Modeling for PDEs and PDEs Modeling for AI

Subtopics

• Numerical analysis with AI methods: Numerical algorithms are increasingly combined with AI to improve the accuracy and efficiency of scientific computations.
• PDE modeling of neural networks: Multi-physics and multiscale modeling leverage AI to handle the interaction of multiple physical processes in a unified framework.
• Learning-enhanced control (neural networks can be used as controllers, or to generate controllers), control-enhanced learning (control of hyperparameters, or of training sets, or of the decision-making).
• Study of stochastic PDE using AI (solvability, control, estimations and inverse problems).
• Neural PDE, PDE inspired designs for neural networks architectures.

Details on the eligibility conditions are specified in the call text available further down this page in the Documents section. The template to be used for project proposals is also available in this section. 

Project proposals must be submitted in parallel by the national coordinators on the ANR and DST submission platforms, in compliance with the respective required formats and submission procedures.

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