Machine Learning for Quantum Simulations

Supervisor:

Johannes Stork, Division of Computer Science
Danny Thonig, Division of Mathematics

Background:

Atomistic spin dynamics (ASD) enables simulations of magnetic materials at the atomic scale by resolving the interactions and time evolution of individual magnetic moments. The underlying dynamics is governed by an effective magnetic field originating from quantum-mechanical interactions. However, the complexity of the quantum description and its mathematical formulation limits the scalability of ASD toward large and computationally demanding systems. To address this challenge, we aim to employ machine-learning techniques to approximate the quantummechanical contributions and use neural networks to predict the intrinsic effective magnetic field within ASD simulations. This approach is expected to significantly accelerate large-scale magnetic modelling while retaining essential quantum accuracy.

Objective:

The goal of this thesis is to develop a scalable neural network capable of predicting intrinsic magnetic fields from a given configuration of atomic magnetic moments and to integrate this model into an atomistic spin-dynamics framework.

Tasks:

1. Literature Review and Technology Familiarization
Survey relevant literature on atomistic spin dynamics, effective-field formalisms, and machine-learning approaches for physical modelling. Gain a solid mathematical understanding of the existing ASD framework and the associated codebase. Review neural-network architectures, training strategies, and suitable loss functions for vector-field prediction.
2. Producing training data
For selected small magnetic systems (e.g., dimers, trimers, short chains), generate reliable datasets from a “black box” linking magnetic-moment configurations to intrinsic fields, energies, and moment magnitudes. These data will form the basis for supervised learning. No knowledge about quantum mechanics needed. 3. Identify suitable descriptors Identify and construct physically meaningful descriptors that represent local magnetic environments and preserve relevant symmetries.
4. Design the network and train it
Develop a scalable neural-network model, train it on the generated datasets, and evaluate its accuracy and generalization.
5. Interface the network to the atomistic spin dynamics code
Implement an interface that allows the trained network to replace or augment the intrinsic-field computation within the atomistic spin-dynamics code, enabling hybrid or fully ML-driven simulations.
6. Documentation and Thesis Writing
Document code changes and usage instructions. Write a comprehensive thesis detailing the methodology, implementation, results, and conclusions.

Expected Outcome:

• A neural network that predicts local effective magnetic fields from atomic magnetic-moment configurations with reasonable accuracy for small benchmark systems.
• A working interface that allows the ASD code to query the neural network during simulations, demonstrating a first proof-of-concept for ML-driven spin dynamics.
• Comparisons showing how well the ML model reproduces intrinsic fields, energies, and dynamical trajectories relative to analytical or quantum-mechanical reference calculations.
• Evidence—at least on test systems—that the ML surrogate offers computational savings compared to direct quantum-mechanical evaluations.

Prerequisites:

• Programming skills in Python or, preferably, in C++
• Familiarity with basic machine learning concepts and software like PyTorch
• Interest in high-performance computing and scientific simulations