WP1 includes all requirements that ensure compliance with the ethical principles and applicable international, EU and national law in the proposed research and training activities.

Main objectives: 2.1 Recruitment and IN-DEEP enrollment strategy. 2.2 Formulation of the nine individual research projects. 2.3 Training Development Programme. 2.4 Progress monitoring of each doctoral candidate.

Main objectives: 3.1 Analyze stability, approximation properties, and convergence of Deep PDE solvers. 3.2 Design novel losses for solving PDEs using Deep Learning. 3.3 Develop uncertainty estimation and local explainability techniques to validate Deep PDE solvers. 3.4 Design adaptive strategies for Deep PDE solvers. 3.5 Develop hybrid methods combining traditional numerical methods and DL.

Main objectives: 4.1 Generate massive databases for training parametric PDEs. 4.2 Develop efficient adaptive training algorithms for Deep parametric PDE solvers. 4.3 Develop Graph Neural Network architectures for Deep parametric PDE solvers. 4.4 Study approximation properties of Deep parametric PDE solvers. 4.5 Validate Deep parametric PDE solvers with traditional numerical methods.

Main objectives:  5.1 Calibrate and enrich a PDE from collected data using Physics-Informed Neural Networks. 5.2 Develop automated strategies for enhancing learning in inverse problems governed by PDEs. 5.3 Guarantee the uniqueness of the solution of the parameterized inverse problem and the convergence in DL-based methods. 

Main objectives: 6.1 Solve inverse problems governed by PDEs arising in geophysics: interpret experimental measurements to map a region of the Earth’s subsurface. 6.2 Solve inverse problems governed by PDEs relevant for smart-city applications: invert experimental measurements to assess the structural health of civil and industrial infrastructures. 6.3 Solve inverse problems governed by PDEs with health applications: interpret collected data for patient-specific predictions of tumor growth and treatment response.

Main objectives: 7.1 Data protection plan. 7.2 Plan for exploitation and dissemination of results.  7.3 Dissemination to the research community. 7.4 Transfer of knowledge to institutions and industry. 7.5 Communication and dissemination to the society at large.

WP8 includes all management activities and the setup process to ensure that the project reaches the planned objectives in terms of expected technical outputs, recruitment and training of the doctoral candidates, schedule, and resource use. As project leader, UPV/EHU will coordinate the overall structure of the project.