The field of computational methods for quantum chemistry and related areas is experiencing significant advancements, driven by the development of innovative techniques that improve scalability, accuracy, and efficiency. A key direction is the integration of machine learning and physical insights to enhance the solution of high-dimensional partial differential equations, which is crucial in various fields such as quantum chemistry, economics, and finance. Another important trend is the refinement of approximate solutions during inference, leading to improved convergence rates and reduced errors. Furthermore, the repurposing of pre-trained models for simulation-based inference is showing promise in achieving accurate results with minimal simulations, which is particularly important for expensive simulators. Noteworthy papers in this area include:

• Toward optimal-scaling DFT, which presents a mathematical analysis of stochastic density functional theory with nearly-optimal scaling.
• Physics-Informed Inference Time Scaling via Simulation-Calibrated Scientific Machine Learning, which introduces a framework that dynamically refines and debiases predictions during inference.
• Effortless, Simulation-Efficient Bayesian Inference using Tabular Foundation Models, which proposes a method for achieving accurate inference with few simulations by leveraging pre-trained autoregressive conditional density estimators.