# My Research

#### The 10,000 foot view

I am interested in developing better (faster, more accurate, more general) algorithms for solving the electronic structure problem and other quantum many-body 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.

On the algorithmic side, questions that interest me include:

- How can we efficiently solve the very high dimensional partial differential equations that arise from interacting quantum matter?
- Which sorts of systems are computationally tractable to simulate, and which are not?
- Can neural networks help us to simulate systems that are hard to simulate using traditional methods?

On the applications side, I’m excited about the potential impact of these algorithms on:

- The development of 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 current 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. Work is ongoing to develop a better theoretical understanding of SPRING and to develop other algorithms based on the same underlying connection.

#### 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,*arXiv*2024

Software: