Degree Awarding Institutions: Kungliga Tekniska Hoegskolan, Sweden & Bergische Universitaet Wuppertal, Germany | Supervision: D. Pleiter and A. Frommer | Planned Secondments: The Cyprus Institute - training on LQCD application software; Hewlett Packard Enterprise - training on HPC architectures.

Objectives: The goal is to investigate the potential of new programming models for exploiting new hardware architectures in HPC with the aim to balance programming effort and achieved performance as the complexity and diversity of architectures increases. Specifically, this project will: i) provide application-level benchmarks based on algorithms used in lattice QCD (LQCD) exploiting different task-based programming models; ii) use and enhance metrics for performance-portability and explore performance-portability for application-level benchmarks; and iii) establish performance bounds, to identify shortcomings of existing programming models.

Expected Results:

1. Efficient implementation of key LQCD kernels for different programming models and hardware architectures
2. Metrics for assessing performance-portability
3. Proof-of-concept integration in an established LQCD application framework, showing performance benefits on relevant architectures as well as enhanced performance-portability

Degree Awarding Institutions: Bergische Universitaet Wuppertal, Germany & University of Cyprus, Cyprus | Supervision: A. Frommer and K. Kahl; C. Alexandrou | Planned Secondments: NVIDIA - HPC and ML programming; Hewlett Packard Enterprise - training on exascale systems.

Objectives: To develop novel, optimal combinations of stochastic and probing methods, which are used to compute the trace of a matrix function f(A). Specifically: i) use ML to fit stochastically generated samples to a surrogate model; ii) use ML to determine the decay of f(A) w.r.t. the distance from the diagonal, as is required in the standard probing approach; and iii) substantiate the improvements via theoretical analysis and demonstrate its relative merits for several application areas, including large-scale problems from QCD and ML.

Expected Results:

1. New stochastic techniques to compute and assess the quality of approximate distance-d colorings for probing methods
2. Analysis of the decay of f(A) away from the graph of A in the presence of deflation
3. A general algorithmic framework, which combines stochastic (multilevel) Monte Carlo with improved probing techniques
4. Efficient computation of f(A) and decay behavior of these functions using surrogate models and ML adapted to special applications
5. Further improvement for special situations, in particular for multilinear problems formulated in tensor representation
6. Demonstration of the efficiency gains for selected applications

Degree Awarding Institutions: Bergische Universitaet Wuppertal, Germany & The Cyprus Institute, Cyprus | Supervision: K. Kahl and A. Frommer; M. Nicolaou and S. Bacchio | Planned Secondment: SIDACT - use of statistical learning in commercial applications, including crash test simulations.

Objectives: Study the ML nature of algebraic multigrid (AMG) methods, that are optimally fast solvers for discretizations of a class of partial differential equations (PDEs) in applications including lattice QCD (LQCD). Specifically we will: i) use statistical learning theory to establish control over the performance potential and convergence of the AMG setup process; ii) identify interfaces in the statistical framework of adaptive AMG that enable the input of expert knowledge, thus accelerating, not only the resulting multigrid method, but also its setup; iii) apply these approaches to improve the performance of AMG in LQCD and, in particular, improve the scaling of multigrid methods, especially on GPU systems and accelerate the convergence of the coarsest-grid linear system.

Expected Results:

1. Derive a connection between statistical ML and the adaptive setup of AMG, enabling both a deeper understanding of the potential performance of AMG and providing new techniques to improve their quality and cost
2. Improve efficiency of the AMG setup, improving data generation and usage for tuning the components and providing statistical modeling to further reduce the computational cost of the setup
3. Develop interfaces to improve the efficiency of AMG, including its setup, by incorporating, e.g., appropriate statistical modeling, inherent symmetries, and invariances, with emphasis on LQCD
4.  Implement outcomes in existing LQCD open software (e.g., DDαAMG and/or QUDA) for simulations at physical values of the light quark masses

Degree Awarding Institutions: The Cyprus Institute, Cyprus & Technische Universitaet Berlin, Germany | Supervision: G. Koutsou and J. Finkenrath; K. R. Muller and P. Kessel | Planned Secondments: DESY - training on trivializing maps; NVIDIA - parallel ML codes.

Objectives: Apply flow-based generative models for accelerating the simulation of lattice gauge theories (LGT), in particular for assessing scalability in demanding systems, such as QCD. The particular objectives are to: i) apply the models to φ4 and the Schwinger model, studying their scalability as the problem size increases and as critical points are approached; ii) study their relation to the so-called trivializing maps (M. Luscher, arXiv:0907.5491) and investigate informing training using this relation; iii) use domain decomposition techniques adapted to models for improving volume scaling, as well as scalability of parallel implementations on multi-GPU systems; and iv) apply similar approaches to standard sampling techniques, such as during the molecular dynamics (MD) evolution within Hybrid Monte Carlo updates.

Expected Results:

1. Implement generative flows for the simulating LGTs and determine their scalability with respect to the volume and approach to criticality
2. Develop physics informed pre-training, transfer learning techniques, and symmetry preserving architectures for these models
3. Develop parallel ML codes for distributed training of the models on parallel GPU systems, using methods that facilitate this, such as domain decomposition

Degree Awarding Institutions: Telecom Paris - Institut Mines-Telecom, France & Universita degli Studi di Roma "Tor Vergata", Italy | Supervision: K. Um; L. Biferale; M. Desbrun | Planned Secondment: SIDACT - mentoring on applications of ML algorithms in automobile industry.

Objectives: Develop methods for reconstructing highly complex space-time turbulent flows out of a partial set of field measurements via data assimilation (DA). In particular: i) use cutting-edge learning techniques such as PINNs and differentiable physics for data assimilation; ii) use Rayleigh-B´enard flows, tuning the ratio between the inertial and buoyant forces, to test the technique; iii) evaluate their performance with respect to the quality and quantity of the data provided; and iv) study the possibility to develop new metrics based on deep features for spatiotemporal turbulent flow data. A massively parallel in-house Lattice Boltzmann algorithm will be used to generate ground truth data, and ML-CFD interfaces will be developed in collaboration with ESR12 and ESR13.

Expected Results:

1. Validation of new ML tools for DA of strong convection
2. Quality and quantity assessment of DA performance, including Eulerian vs Lagrangian approaches
3. Development of new metrics based on deep features for spatiotemporal DA

Degree Awarding Institutions: Kungliga Tekniska Hoegskolan, Sweden & Rheinisch-Westfälische Technische Hochschule Aachen University, Germany | Supervision: E. Lindahl; P. Carloni | Planned Secondment: Fondazione Istituto Italiano di Tecnologia, Genova - training on ML methods for interatomic potentials.

Objectives: Advance free energy calculations, which have the potential to directly predict binding energies or which structures/states molecules will adapt, focusing on recent challenges that emerged in the use of ML trained on QM data. The specific objectives are to: i) implement efficient algorithms to make potentials extracted from NNs smooth and differentiable when applied to simulations in GROMACS, primarily by improving, parallelizing, and accelerating on GPUs the calculations of the influence functions which model the environment of each atom; and ii) implement an interface allowing arbitrary inference-based forces to contribute to simulations where the rest of the system uses molecular dynamics (MD), and train NNs to improve structure refinement by learning from intermediate-resolution experimental cryo-EM electron densities.

Expected Results:

1. Accelerated algorithms, on GPUs, that allow for smooth and differentiable potentials extracted from NNs
2. Trained networks for improved structure refinement by learning from intermediate-resolution experimental cryo-EM electron densities
3. New interfaces in GROMACS allowing arbitrary inference-based forces contributing to simulations that are otherwise performed with MD

Degree Awarding Institutions: Universita degli Studi di Padova, Italy & University of Cyprus, Cyprus | Supervision: S. Montangero; C. Alexandrou and H. Panagopoulos | Planned Secondments: DESY - training on LGTs; CINECA - HPC optimization of tensor network code; Qruise - training on QC architectures.

Objectives: We will develop a tensor network-based QC simulator integrated on HPC systems, addressing the need for methods to benchmark quantum computers of intermediate scale which are seeing a rapid increase in qubits, currently in the range of 50-200 qubits. Simulation of tens of qubits is impossible for exact classical simulations and is a major challenge for the most sophisticated tensor network codes available. To address this challenge we will: i) develop tensor network methods that can exploit HPC; ii) implement lattice gauge theories (LGTs), from QED to extensions to low dimensional theories, e.g. non-abelian gauge theories, as a benchmark for QC hardware; and iii) evaluate the developed benchmark on upcoming exascale systems.

Expected Results:

1. A tensor network HPC simulator of a quantum computer
2. Study of the efficiency and scalability of digital quantum simulations of LGTs emulated on HPC systems

Degree Awarding Institutions: Universita degli Studi di Padova, Italy & University of Cyprus, Cyprus | Supervision: S. Montangero; H. Panagopoulos | Planned Secondments: DESY - LQCD simulations; IBM - porting on IBM QC hardware.

Objectives: Enable simulations of (2+1)D and (3+1)D QED using tensor networks and quantum computers, with particular objectives to: i) employ a Hamiltonian formulation for QED, allowing its simulation via tensor networks, including a non-zero chemical potential and a topological term, as has recently been derived (see arXiv:2008.09252); ii) study the system in (2+1)D and (3+1)D using tensor networks and also QC for the (2+1)D case; iii) collaborate with ESR7 on using the QC simulator to prepare simulations on a quantum hardware.

Expected Results:

1. Determination of the phase diagram and phase transitions of QED in the presence of a chemical potential and a topological term
2. Evaluation of the low-lying energy spectrum by computing the mass gap of the theory in the various phases

Degree Awarding Institutions: Technische Universitaet Berlin, Germany & Universita degli Studi di Padova, Italy | Supervision: K. R. Muller and P. Kessel; S. Montangero | Planned Secondment: Qruise - application of quantum ML to quantum control of quantum hardware.

Objectives: Compare quantum and quantum-inspired ML to traditional approaches based on deep neural networks (DNNs) and kernel learning, focusing on largescale ML tasks with applications in computer vision, quantum chemistry, optimization and denoising of quantum circuits. The particular objectives are to: i) use large-scale tensor network simulations of quantum circuits which, depending on the entanglement of the underlying system, allow for up to 100 qubits; ii) investigate extensions of quantum-inspired explainability methods, such as techniques based on entanglement entropy, to more traditional ML methods with emphasis on interpretability; iii) explore applications, e.g. in quantum chemistry, building on classical molecular kernel learning methods, and in quantum systems, harnessing quantum-inspired or classical generative models. An additional advantage is that the learnt noise mitigation strategies can be included in the model architecture.

Expected Results:

1. Benchmarking and quantitative comparison of quantum-based vs classical ML
2. Application of the developed methods to big-data tasks, such as image recognition and quantum physics
3. Analysis of the interpretability of the respective methods

Degree Awarding Institutions: University of Cyprus, Cyprus & Bergische Universitaet Wuppertal, Germany | Supervision: C. Alexandrou; A. Frommer and K. Kahl | Planned Secondment: NVIDIA - mentoring on efficient GPU implementation of multi-level algorithm.

Objectives: Compute precisely key quantities of central importance to the search for physics beyond the standard model and, in particular, the muon anomalous moment gμ-2 that is being measured at Fermilab and currently differs from the experimental value by about four standard deviations. To accomplish this goal we will: i) calculate connected and disconnected contributions, including isospin breaking with our ETMC collaborators, employing improved algebraic multigrid (AMG) methods; ii) incorporate further improvements resulting from ESR2 for the trace optimized for GPUs; and iii) employ scalable multigrid solvers by ESR3 that will further accelerate the inversions and increase the precision.

Expected Results:

1. Assessment of improvements of new algorithms for AMG (ESR3) to speed up inversions and trace evaluation (ESR2) for loops
2. Computation of gμ-2 to a precision 3-4 per mil in the continuum limit, needed for meaningful comparison with experiments

Degree Awarding Institutions: University of Cyprus, Cyprus & Technische Universitaet Berlin, Germany | Supervision: H. Panagopoulos and C. Alexandrou; P. Kessel | Planned Secondment: RetailZoom - mentoring on using HPC and ML for the retail sector.

Objectives: Compute key quantities of central importance to the experimental program of the future Electron Ion Collider (EIC), such as generalized parton distributions (GPDs) using the large momentum effective theory. GPDs require the computation of matrix elements of extended operators with the nucleon boosted to large momentum leading to exponentially increasing statistical errors as the momentum increases. To address the noise increase we will: i) use ML approaches for noise reduction (arXiv:1807.05971) for improving the accuracy as we increase the boost; ii) employ ML-inspired multigrid solvers to be developed by ESR3 and better algorithms for trace estimation by ESR2 to further improve accuracy and allow for the flavor decomposition of GPDs that requires the computation of disconnected diagrams with extended operators; and iii) investigate the renormalization of the required extended operators, taking into account the mixing of the isoscalar and gluon GPDs. 

Expected Results:

1. Computation of the unpolarised, helicity and transversity GPDs for an ensemble of twisted mass fermions at the physical point and at non-zero skewness

Degree Awarding Institutions: Universita degli Studi di Roma ”Tor Vergata”, Italy & Telecom Paris - Institut Mines-Telecom, France | Supervision: L. Biferale; K. Um; M. Desbrun | Planned Secondment: NVIDIA - mentoring on the efficient implementation of solver-in-the-loop algorithms.

Objectives: Investigate new ML-based approaches to perform a posteriori training of optimal sub-grid modeling for large eddy simulations of strongly turbulent flows, ensuring a fully model-consistent training, where the model sees its own outputs as inputs. The approach consists of performing the ML calibration based on how the errors produced by the model are propagated by the governing dynamics. Specifically, we aim to: i) employ a solver-in-the-loop method exploiting recent fast auto-differentiation algorithms to evaluate the backpropagation of errors through the discretized simulation; ii) develop and validate the approach on 2D models for natural convection flows; and iii) apply it for state-of-the-art three-dimensional (3D) simulations of realistic 3D Rayleigh-Benard convection cells. This new solver-in-the-loop training has demonstrated its great potential in learning tasks where the model has to take into account its recurrent inferences and its influence. Collaborations and synergies with ESR5 and ESR13 will also take place concerning the development of the ML-CFD interface.

Expected Results:

1. Validation of new solver-in-the-loop approaches for sub-grid modeling of 2D and 3D natural convection simulations
2. Comparison against other dynamic sub-grid-modelling approaches
3. Optimal discretization schemes for speeding up CFD simulations

Degree Awarding Institutions: The Cyprus Institute, Cyprus & Universita degli Studi di Roma "Tor Vergata", Italy & Telecom Paris - Institut Mines-Telecom, France  | Supervision: N. Savva and M. Nicolaou; M. Sbragaglia and R. Benzi; K. Um | Planned Secondment: Hewlett Packard Enterprise - mentoring on the efficient implementation of Lattice Boltzmann algorithms.

Objectives: To develop AI-driven methodologies to uncover nonlinear mappings between the behaviours of droplets on surfaces and the features that control them. Specifically we aim to develop: i) novel methodologies inspired from recently proposed NN architectures that have been employed in other settings, including, for example, DeepOnets and the Fourier Neural Operator; and ii) Computational Fluid Dynamics (CFD) high-fidelity codes based on the Lattice Boltzmann method to provide the ground truth data for training.

Expected Results:

1. ML-augmented modeling of multi-phase and multi-component droplet dynamics in complex environments applied for the first time in Lattice Boltzmann simulations, which allows us to mitigate the computing costs associated with parametric studies of high-fidelity CFD simulations
2. Novel AI-assisted workflows for uncovering optimal droplet transport mechanisms

Degree Awarding Institutions: Forschungszentrum Julich GmbH, Germany & Rheinisch-Westfälische Technische Hochschule Aachen University, Germany & Kungliga Tekniska Hoegskolan, Sweden | Supervision: P. Carloni; E. Lindahl | Planned Secondment: Fondazione Istituto Italiano di Tecnologia, Genova - training on normalizing flow networks to learn structure representation.

Objectives: Employ normalizing flows to improve free energy calculations22 in synergy with ESR6. Specifically we aim to: i) extend the present QM/MM interface in GROMACS with ML/MM support, modeling part of the interactions in the system with inference-based potentials; ii) develop an iterative and data-efficient strategy to train accurate representation of the QM/MM interatomic potential at an accurate (target) level of theory by combining a simple reference potential with normalizing flow NNs; iii) perform free energy calculations exploiting the ML/MM potentials through a combination of simulation and targeted perturbation methods.

Expected Results:

1. ML/MM implementation in GROMACS; ii) an iterative method for refining ML potential representations

Degree Awarding Institutions: Forschungszentrum Julich GmbH, Germany & Rheinisch-Westfälische Technische Hochschule Aachen University, Germany & Kungliga Tekniska Hoegskolan, Sweden | Supervision: G. Rossetti and P. Carloni; E. Lindahl | Planned Secondment: Fondazione Istituto Italiano di Tecnologia, Genova - training on the basics of the method and its implementation.

Objectives: Study the protein/protein interface energetics of the insulin dimer by means of free energy calculations performed using ML/MM potentials. The key issues of code scalability and the time scale problem will be addressed for the first time using a recently developed method that builds on metadynamics - an exact method to compute free energies - and the statistical mechanics of paths. The method applies to stochastic trajectories and its theoretical underpinning is the Onsager-Machlup action that determines the path probability distribution. It maps the time scale problem that limits the statistical accuracy of current approaches into a size problem in an auxiliary, enlarged configurational space, which allows using massively parallel computer architectures to tackle the time scale problem.

Expected Results:

1. Investigation of the protein-protein interface energetic interaction for the case of the insulin dimer
2. A ML/MM potential model applicable to study protein-protein interfaces