Andrés Guzmán-Cordero

Density functional theory (DFT) strikes a practical balance between accuracy and computational cost in many problems of computational chemistry and materials science. However, many DFT calculations are limited by fixed atom-centered basis sets, which dictate how accuracy and cost scale with system size. We propose Gaussian Splatting for Density Functional Theory (GS-DFT), which represents molecular orbitals as a cloud of Gaussians whose positions, shapes, and mixing coefficients are optimized jointly by gradient descent to minimize the energy without training data. Conceptually, GS-DFT is 3D Gaussian splatting with the renderer replaced by quantum mechanics. We introduce two key solver components: adaptive density fitting with screening for efficient evaluation of two-electron integrals, and a regularized differentiable orthogonalization of the molecular orbitals. Empirically, the optimized basis reaches the accuracy of the largest conventional basis sets with a fraction of the parameters, converging systematically in energy, density, and nuclear forces. At equal parameter count, it captures the stretched-bond and anion physics that fixed bases only recover with specialized basis augmentation. The resulting solver exhibits quadratic peak memory scaling in the cloud size, allowing us to simulate systems of up to 2,742 atoms (10,406 electrons) without any modifications at triple-zeta scale using a single four-GPU node.

Natural gradient methods significantly accelerate the training of Physics-Informed Neural Networks (PINNs), but are often prohibitively costly. We introduce a suite of techniques to improve the accuracy and efficiency of energy natural gradient descent (ENGD) for PINNs. First, we leverage the Woodbury formula to dramatically reduce the computational complexity of ENGD. Second, we adapt the Subsampled Projected-Increment Natural Gradient Descent algorithm from the variational Monte Carlo literature to accelerate the convergence. Third, we explore the use of randomized algorithms to further reduce the computational cost in the case of large batch sizes. We find that randomization accelerates progress in the early stages of training for low-dimensional problems, and we identify key barriers to attaining acceleration in other scenarios. Our numerical experiments demonstrate that our methods outperform previous approaches, achieving the same L² error as the original ENGD up to 75× faster.

While denoising diffusion and flow matching have driven major advances in generative modeling, their application to tabular data remains limited, despite its ubiquity in real-world applications. To this end, we develop TabbyFlow, a variational Flow Matching (VFM) method for tabular data generation. To apply VFM to data with mixed continuous and discrete features, we introduce Exponential Family Variational Flow Matching (EF-VFM), which represents heterogeneous data types using a general exponential family distribution. We hereby obtain an efficient, data-driven objective based on moment matching, enabling principled learning of probability paths over mixed continuous and discrete variables. We also establish a connection between variational flow matching and generalized flow matching objectives based on Bregman divergences. Evaluation on tabular data benchmarks demonstrates state-of-the-art performance compared to baselines.

We discuss how machine learning researchers view and approach problems in chemistry and provide our considerations for maximizing impact when researching machine learning for chemistry.

Molecules are three-dimensional objects, so it is tempting to assume that 3D representations should dominate 1D and 2D ones for molecular discovery. We test that assumption inside a Bayesian optimization loop, where what matters is not representation faithfulness but whether the induced posterior finds high-value molecules in few expensive evaluations. Comparing Gaussian processes against neural surrogates with a linearized Laplace approximation, and scoring by normalized GAP, we find that richer geometry adds cost faster than it adds decision-making power.