Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flows
This work addresses the challenge of efficient sampling in Quantum Field Theory for physicists, representing a strong domain-specific advancement.
The authors tackled the problem of sampling from high-dimensional probability distributions in Quantum Field Theory by proposing a shallow continuous normalizing flow that incorporates symmetries, resulting in a significant improvement in sampling efficiency, with effective sample size increasing from 1% to 66% compared to a realNVP baseline on a 32x32 lattice.
We propose a continuous normalizing flow for sampling from the high-dimensional probability distributions of Quantum Field Theories in Physics. In contrast to the deep architectures used so far for this task, our proposal is based on a shallow design and incorporates the symmetries of the problem. We test our model on the $φ^4$ theory, showing that it systematically outperforms a realNVP baseline in sampling efficiency, with the difference between the two increasing for larger lattices. On the largest lattice we consider, of size $32\times 32$, we improve a key metric, the effective sample size, from 1% to 66% w.r.t. the realNVP baseline.