My Research
The 10,000 foot view
I am interested in developing better (faster, more accurate, more general) algorithms for leveraging deep neural networks to solve scientific problems. This field is very exciting because it lies at the intersection of some extremely challenging and fundamental computational problems and a wide variety of important scientific and technological applications. I am particularly interested in the use of neural network wavefunctions to simulate quantum systems, but also dabble in other areas such as physics-informed neural networks and machine-learned interatomic potentials.
On the algorithmic side, questions that interest me include:
- What are the best algorithms for training neural networks to solve scientific simulation problems?
- How can we overcome the stochasticity and ill-conditioning inherent in training neural networks in order to find highly accurate solutions to scientific problems?
- How can neural networks help us to efficiently solve the very high dimensional partial differential equations that arise from interacting quantum matter?
On the applications side, I’m excited about the potential impact of these algorithms on:
- Basic energy science
- Clean energy technologies like batteries, artificial photosynthesis, clean nitrogen, and carbon capture
- Biochemistry from fundamental science to drug development
- Quantum computers, quantum sensors, and other quantum technologies
The view from the trenches
My current research focuses on the use of neural networks to represent ground-state wavefunctions for small but strongly correlated atoms and molecules. The pitch here is that neural network wavefunctions can allow us to find nearly exact ground-state wavefunctions for very challenging problems where other algorithms based on chemical heuristics fail. The challenge is that neural network training is very expensive and very stochastic, making it hard to attain the high accuracies that are required for making useful chemical predictions. There is a great deal of exciting recent and ongoing work aiming to develop better network architectures, training algorithms, and software which I believe will ultimately enable neural network wavefunctions to make a large impact in the field of quantum chemistry.
Within the field of neural network wavefunctions, my focus is on developing better training algorithms. Specifically, along with my advisor and several 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 shown promising results for neural network wavefunctions and may also be applicable to other scientific domains. Recent works have provided a better theoretical understanding of SPRING, and ongoing work is targeted at using this understanding to develop new and more powerful optimizers based on similar ideas.
References on neural network wavefunctions
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 2020
A few selected exciting developments:
- I. Glehn, J. Spencer, D. Pfau, A self-attention ansatz for ab-initio quantum chemistry, 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. Goldshlager, N. Abrahamsen, L. Lin, A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions, Journal of Computational Physics 2024
Software: