Scale the architecture to larger particle systems and higher-dimensional configuration spaces

Scale and optimize the neural network structure and training procedure so that the amortized sampler can handle larger particle counts and configuration spaces of higher dimension beyond the demonstrated 64-dimensional interacting-particle proof of concept.

Background

The high-dimensional experiment demonstrates the method on a 64-dimensional interacting-particle system using pair-probe sensors and an equivariant particle-flow decoder. The authors characterize this experiment as a proof of concept rather than an extensively optimized large-scale implementation.

The unresolved challenge is to scale the architecture and training methodology to systems with more particles and higher-dimensional configuration spaces.

References

The main open challenges are scaling to larger particle systems and handling more complex and costly energy functions.

— Neural Transport Nested Sampling  (2609.29413 - Yallup et al., 24 Sep 2026) in Section 1, Conclusion

Even so, NTNS is the only method that comes close on LJ-55, and we conjecture it has the best chance to scale to the harder classical target.

— Neural Transport Nested Sampling  (2609.29413 - Yallup et al., 24 Sep 2026) in Appendix, Section 8, Phase-Diagram Analysis

Lastly, our experiments in higher dimensions are only a proof of concept. The network structure and training procedure have not been extensively optimized. Scaling to larger particle counts and configuration spaces of higher dimension remains an important challenge.

— Deep operator learning for efficient sampling from invariant measures of stochastic differential equations  (2609.11376 - Guo et al., 10 Sep 2026) in Section 7, Conclusion