Overview
I aim to develop the algorithmic toolbox to enable deep neural networks to solve challenging quantum many-body problems. This direction is known as “neural quantum states,” or alternatively “neural network wavefunctions.”
On the algorithmic side, questions that interest me include:
- What kinds of optimizers are suitable for attaining precise scientific solutions while optimizing millions of variational parameters?
- What kinds of network architectures are suitable for attaining precise scientific solutions to high-dimensional problems, while enforcing physical symmetries?
On the applications side, I am excited about the potential impact of this technology on:
- Basic energy science, including transition metal chemistry which has long resisted accurate simulation.
- Clean energy technologies like batteries, artificial photosynthesis, clean nitrogen, and carbon capture.
- Quantum computers, quantum sensors, and other quantum technologies.
Specifics
My current focus is on developing better optimizers for neural quantum states. Specifically, along with a number of wonderful collaborators, I am working to exploit a previously unappreciated connection between neural network optimization and randomized numerical linear algebra. This connection has enabled us to develop the SPRING algorithm, which has been used to power some of the largest neural quantum simulations to date, and which is also applicable to other scientific domains. Our more recent works have established a stronger theoretical and conceptual foundation for SPRING, and ongoing work aims to use this foundation to develop new and even more powerful optimizers based on similar ideas.
References
Review article:
- J. Hermann et al, Ab initio quantum chemistry with neural-network wavefunctions, Nature Reviews Chemistry (2023).
Trailblazers of the field:
- G. Carleo and M. Troyer, Solving the Quantum Many Body Problem with Artificial Neural Networks, Science (2017).
- J. Hermann, Z. Schätzle, F. Noé, Deep-neural-network solution of the electronic Schrödinger equation, Nature Chemistry (2020).
- D. Pfau, J. Spencer, A. Matthews, W. Foulkes, Ab initio solution of the many-electron Schrödinger equation with deep neural networks, Physical Review Research (PRR 2020).
A few selected exciting developments:
- I. Glehn, J. Spencer, D. Pfau, A self-attention ansatz for ab-initio quantum chemistry, International Conference on Learning Representations (ICLR 2023).
- R. Li et al, A computational framework for neural network-based variational Monte Carlo with Forward Laplacian, Nature Machine Intelligence (2024).
- A. Chen, M. Heyl, Empowering deep neural quantum states through efficient optimization, Nature Physics (2024).
- G.G., N. Abrahamsen, L. Lin, A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions, Journal of Computational Physics (JCP 2024).
Software: