Luca Thiede

Alexandra Volokhova, Michał Koziarski, Alex Hernández-García et al.

Sampling diverse, thermodynamically feasible molecular conformations plays a crucial role in predicting properties of a molecule. In this paper we propose to use GFlowNet for sampling conformations of small molecules from the Boltzmann distribution, as determined by the molecule's energy. The proposed approach can be used in combination with energy estimation methods of different fidelity and discovers a diverse set of low-energy conformations for highly flexible drug-like molecules. We demonstrate that GFlowNet can reproduce molecular potential energy surfaces by sampling proportionally to the Boltzmann distribution.

Kirill Neklyudov, Jannes Nys, Luca Thiede et al.

Solving the quantum many-body Schrödinger equation is a fundamental and challenging problem in the fields of quantum physics, quantum chemistry, and material sciences. One of the common computational approaches to this problem is Quantum Variational Monte Carlo (QVMC), in which ground-state solutions are obtained by minimizing the energy of the system within a restricted family of parameterized wave functions. Deep learning methods partially address the limitations of traditional QVMC by representing a rich family of wave functions in terms of neural networks. However, the optimization objective in QVMC remains notoriously hard to minimize and requires second-order optimization methods such as natural gradient. In this paper, we first reformulate energy functional minimization in the space of Born distributions corresponding to particle-permutation (anti-)symmetric wave functions, rather than the space of wave functions. We then interpret QVMC as the Fisher-Rao gradient flow in this distributional space, followed by a projection step onto the variational manifold. This perspective provides us with a principled framework to derive new QMC algorithms, by endowing the distributional space with better metrics, and following the projected gradient flow induced by those metrics. More specifically, we propose "Wasserstein Quantum Monte Carlo" (WQMC), which uses the gradient flow induced by the Wasserstein metric, rather than Fisher-Rao metric, and corresponds to transporting the probability mass, rather than teleporting it. We demonstrate empirically that the dynamics of WQMC results in faster convergence to the ground state of molecular systems.

Jack Richter-Powell, Luca Thiede, Alán Asparu-Guzik et al.

Molecular modeling at the quantum level requires choosing a parameterization of the wavefunction that both respects the required particle symmetries, and is scalable to systems of many particles. For the simulation of fermions, valid parameterizations must be antisymmetric with respect to the exchange of particles. Typically, antisymmetry is enforced by leveraging the anti-symmetry of determinants with respect to the exchange of matrix rows, but this involves computing a full determinant each time the wavefunction is evaluated. Instead, we introduce a new antisymmetrization layer derived from sorting, the $\textit{sortlet}$, which scales as $O(N \log N)$ with regards to the number of particles -- in contrast to $O(N^3)$ for the determinant. We show numerically that applying this anti-symmeterization layer on top of an attention based neural-network backbone yields a flexible wavefunction parameterization capable of reaching chemical accuracy when approximating the ground state of first-row atoms and small molecules.

Luca Thiede, Chong Sun, Alán Aspuru-Guzik

An efficient and expressive wavefunction ansatz is key to scalable solutions for complex many-body electronic structures. While Slater determinants are predominantly used for constructing antisymmetric electronic wavefunction ansätze, this construction can result in limited expressiveness when the targeted wavefunction is highly complex. In this work, we introduce Waveflow, an innovative framework for learning many-body fermionic wavefunctions using boundary-conditioned normalizing flows. Instead of relying on Slater determinants, Waveflow imposes antisymmetry by defining the fundamental domain of the wavefunction and applying necessary boundary conditions. A key challenge in using normalizing flows for this purpose is addressing the topological mismatch between the prior and target distributions. We propose using O-spline priors and I-spline bijections to handle this mismatch, which allows for flexibility in the node number of the distribution while automatically maintaining its square-normalization property. We apply Waveflow to a one-dimensional many-electron system, where we variationally minimize the system's energy using variational quantum Monte Carlo (VQMC). Our experiments demonstrate that Waveflow can effectively resolve topological mismatches and faithfully learn the ground-state wavefunction.

Austin Cheng, Cher Tian Ser, Marta Skreta et al.

Machine learning has been pervasively touching many fields of science. Chemistry and materials science are no exception. While machine learning has been making a great impact, it is still not reaching its full potential or maturity. In this perspective, we first outline current applications across a diversity of problems in chemistry. Then, we discuss how machine learning researchers view and approach problems in the field. Finally, we provide our considerations for maximizing impact when researching machine learning for chemistry.

Luca Thiede, Abdulrahman Aldossary, Andreas Burger et al.

Density functional theory (DFT) is the most widely used method for calculating molecular properties; however, its accuracy is often insufficient for quantitative predictions. Coupled-cluster (CC) theory is the most successful method for achieving accuracy beyond DFT and for predicting properties that closely align with experiment. It is known as the ''gold standard'' of quantum chemistry. Unfortunately, the high computational cost of CC limits its widespread applicability. In this work, we present the Molecular Orbital Learning (MōLe) architecture, an equivariant machine learning model that directly predicts CC's core mathematical objects, the excitation amplitudes, from the mean-field Hartree-Fock molecular orbitals as inputs. We test various aspects of our model and demonstrate its remarkable data efficiency and out-of-distribution generalization to larger molecules and off-equilibrium geometries, despite being trained only on small equilibrium geometries. Finally, we also examine its ability to reduce the number of cycles required to converge CC calculations. MōLe can set the foundations for high-accuracy wavefunction-based ML architectures to accelerate molecular design and complement force-field approaches.

Jonas Elsborg, Luca Thiede, Alán Aspuru-Guzik et al.

We present the Electronic Tensor Reconstruction Algorithm (ELECTRA) - an equivariant model for predicting electronic charge densities using floating orbitals. Floating orbitals are a long-standing concept in the quantum chemistry community that promises more compact and accurate representations by placing orbitals freely in space, as opposed to centering all orbitals at the position of atoms. Finding the ideal placement of these orbitals requires extensive domain knowledge, though, which thus far has prevented widespread adoption. We solve this in a data-driven manner by training a Cartesian tensor network to predict the orbital positions along with orbital coefficients. This is made possible through a symmetry-breaking mechanism that is used to learn position displacements with lower symmetry than the input molecule while preserving the rotation equivariance of the charge density itself. Inspired by recent successes of Gaussian Splatting in representing densities in space, we are using Gaussian orbitals and predicting their weights and covariance matrices. Our method achieves a state-of-the-art balance between computational efficiency and predictive accuracy on established benchmarks. Furthermore, ELECTRA is able to lower the compute time required to arrive at converged DFT solutions - initializing calculations using our predicted densities yields an average 50.72 % reduction in self-consistent field (SCF) iterations on unseen molecules.

Jonas Elsborg, Felix Ærtebjerg, Luca Thiede et al.

We introduce ELECTRAFI, a fast, end-to-end differentiable model for predicting periodic charge densities in crystalline materials. ELECTRAFI constructs anisotropic Gaussians in real space and exploits their closed-form Fourier transforms to analytically evaluate plane-wave coefficients via the Poisson summation formula. This formulation delegates non-local and periodic behavior to analytic transforms, enabling reconstruction of the full periodic charge density with a single inverse FFT. By avoiding explicit real-space grid probing, periodic image summation, and spherical harmonic expansions, ELECTRAFI matches or exceeds state-of-the-art accuracy across periodic benchmarks while being up to $633 \times$ faster than the strongest competing method, reconstructing crystal charge densities in a fraction of a second. When used to initialize DFT calculations, ELECTRAFI reduces total DFT compute cost by up to ~20%, whereas slower charge density models negate savings due to high inference times. Our results show that accuracy and inference cost jointly determine end-to-end DFT speedups, and motivate our focus on efficiency.

Andreas Burger, Luca Thiede, Alán Aspuru-Guzik et al.

Machine learning force fields show great promise in enabling more accurate molecular dynamics simulations compared to manually derived ones. Much of the progress in recent years was driven by exploiting prior knowledge about physical systems, in particular symmetries under rotation, translation, and reflections. In this paper, we argue that there is another important piece of prior information that, thus fa,r hasn't been explored: Simulating a molecular system is necessarily continuous, and successive states are therefore extremely similar. Our contribution is to show that we can exploit this information by recasting a state-of-the-art equivariant base model as a deep equilibrium model. This allows us to recycle intermediate neural network features from previous time steps, enabling us to improve both accuracy and speed by $10\%-20\%$ on the MD17, MD22, and OC20 200k datasets, compared to the non-DEQ base model. The training is also much more memory efficient, allowing us to train more expressive models on larger systems.

Luca A. Thiede, Mario Krenn, AkshatKumar Nigam et al.

Computer-aided design of molecules has the potential to disrupt the field of drug and material discovery. Machine learning, and deep learning, in particular, have been topics where the field has been developing at a rapid pace. Reinforcement learning is a particularly promising approach since it allows for molecular design without prior knowledge. However, the search space is vast and efficient exploration is desirable when using reinforcement learning agents. In this study, we propose an algorithm to aid efficient exploration. The algorithm is inspired by a concept known in the literature as curiosity. We show on three benchmarks that a curious agent finds better performing molecules. This indicates an exciting new research direction for reinforcement learning agents that can explore the chemical space out of their own motivation. This has the potential to eventually lead to unexpected new molecules that no human has thought about so far.

Luca Anthony Thiede, Pratik Prabhanjan Brahma

Trajectory or behavior prediction of traffic agents is an important component of autonomous driving and robot planning in general. It can be framed as a probabilistic future sequence generation problem and recent literature has studied the applicability of generative models in this context. The variety or Minimum over N (MoN) loss, which tries to minimize the error between the ground truth and the closest of N output predictions, has been used in these recent learning models to improve the diversity of predictions. In this work, we present a proof to show that the MoN loss does not lead to the ground truth probability density function, but approximately to its square root instead. We validate this finding with extensive experiments on both simulated toy as well as real world datasets. We also propose multiple solutions to compensate for the dilation to show improvement of log likelihood of the ground truth samples in the corrected probability density function.