arXiv subjects

Kareem Hegazy

Publications and source records attributed to Kareem Hegazy.

10 recordsLinked to original sources

arXiv2026

Neural equilibria for long-term prediction of nonlinear conservation laws

Nonlinear conservation laws govern a broad class of important physical systems in science and industry and are central to scientific machine learning (SciML). Large general-purpose models offer speed, but replacing the numerical and physical structure of solvers often compromises stability, accuracy, and physical faithfulness. Here, we aim to balance the general inductive bias of conservation with the flexibility and speed of neural networks through a conservation-aware SciML backbone, which we call Neural Discrete Equilibrium (NeurDE). NeurDE places machine learning inside a kinetic solver by learning the local equilibrium closure of a Boltzmann formulation. The kinetic solver still performs transport, relaxation, moment recovery, and conservation; the neural network provides only the nonlinear equilibrium target. We test NeurDE on $6$ conserved systems, including three very challenging subsonic, transonic, and supersonic shock systems. NeurDE outperforms state-of-the-art SciML methods, including neural operators and pretrained SciML foundation models that are $10^4$ and $10^6$ times larger, respectively. Most notably, NeurDE improves upon the numerical method from which it is derived. NeurDE therefore provides a compact target for scientific machine learning in conservative simulation: learn the equilibrium law toward which the system relaxes, not the evolution law itself.

cs.LG↗

arXiv2026

Foundation Models for Discovery and Exploration in Chemical Space

Accurate prediction of atomistic, thermodynamic, and kinetic properties from molecular structures underpins materials innovation. Existing computational and experimental approaches lack the scalability required to navigate chemical space efficiently. Scientific foundation models trained on large unlabelled datasets offer a path towards navigating chemical space across application domains. Here, we develop MIST, a family of molecular foundation models with up to an order of magnitude more parameters and data than prior works. Trained using a novel tokenizer, Smirk, which comprehensively captures nuclear, electronic, and geometric information, MIST learns a diverse range of molecules. MIST models have been fine-tuned to predict more than 400 structure-property relationships and have been shown to match or exceed state-of-the-art performance across diverse benchmarks, from physiology to electrochemistry. We demonstrate the ability of these models to solve real-world problems across chemical space from multiobjective electrolyte solvent screening to stereochemical reasoning for organometallics and mixture property prediction. The clearest demonstration of a foundation model is its ability to solve problems that were neither explicit targets of training nor central to the intentions of its developers. We identify olfactory perception mapping as such a problem, and show that MIST accurately predicted scent profiles and learned a hierarchical representation of olfactory space consistent with hyperbolic geometry. We formulated hyperparameter aware Bayesian neural scaling laws which eliminate the need for hyperparameter sweeps at every scale, making training large compute-optimal models feasible on a limited compute budget. The methods and findings presented here represent a significant step towards accelerating materials discovery, design, and optimization using foundation models.

physics.chem-ph↗

arXiv2026

Recency Biased Causal Attention for Time-series Forecasting

Recency bias is a useful inductive prior for sequential modeling: it emphasizes nearby observations and can still allow longer-range dependencies. Standard Transformer attention lacks this property, relying on all-to-all interactions that overlook the causal and often local structure of temporal data. We propose a simple mechanism to introduce recency bias by reweighting attention scores with a smooth heavy-tailed decay. This adjustment strengthens local temporal dependencies without sacrificing the flexibility to capture broader and data-specific correlations. We show that recency-biased attention consistently improves sequential modeling, aligning Transformer more closely with the read, ignore, and write operations of RNNs. Finally, we demonstrate that our approach achieves competitive and often superior performance on challenging time-series forecasting benchmarks.

cs.LG↗

arXiv2026

Machine-Learned Leftmost Hessian Eigenvectors for Robust Transition State Finding

The reliable determination of transition states (TSs) benefits from second-order information for robust convergence and validation, but the computational expense of Hessians prohibits their routine use in TS optimization. Here, we present a machine-learning-driven TS optimizer that directly predicts the leftmost Hessian eigenvector (LMHE), the critical mode that locally approximates the reaction coordinate encompassing the TS. We demonstrate that our LMHE optimizer recovers TS solutions at the same rate as full Hessian optimizers, and more robustly from degraded initial guess geometries, thereby eliminating the excessively long wall times characteristic of full-Hessian approaches and reducing total gradient evaluations compared to standard quasi-Newton methods. We further improve accuracy and robustness using uncertainty quantification for identifying occasional LMHE prediction failures, that then falls back to a full Hessian update from the machine learned potential at that optimization step, avoiding expensive active learning. Overall our methodology and semi-automated workflow delivers second-order stability at first-order computational expense to provide a highly efficient engine for high-throughput reaction discovery.

physics.chem-ph↗

arXiv2026

The False Promise of Zero-Shot Super-Resolution in Machine-Learned Operators

A core challenge in scientific machine learning, and scientific computing more generally, is modeling continuous phenomena which (in practice) are represented discretely. Machine-learned operators (MLOs) have been introduced as a means to achieve this modeling goal, as this class of architecture can perform inference at arbitrary resolution. In this work, we evaluate whether this architectural innovation is sufficient to perform "zero-shot super-resolution," namely to enable a model to serve inference on higher-resolution data than that on which it was originally trained. We comprehensively evaluate both zero-shot sub-resolution and super-resolution (i.e., multi-resolution) inference in MLOs. We decouple multi-resolution inference into two key behaviors: 1) extrapolation to varying frequency information; and 2) interpolating across varying resolutions. We empirically demonstrate that MLOs fail to do both of these tasks in a zero-shot manner. Consequently, we find MLOs are not able to perform accurate inference at resolutions different from those on which they were trained, and instead they are brittle and susceptible to aliasing. To address these failure modes, we propose a simple, computationally-efficient, and data-driven multi-resolution training protocol that overcomes aliasing and that provides robust multi-resolution generalization.

cs.LG↗

arXiv2023

Applying Bayesian Inference and deterministic anisotropy to retrieve the molecular structure $|Ψ(\boldsymbol{R})|^2$ distribution from gas-phase diffraction experiments

Currently, our general approach to retrieving molecular structures from ultrafast gas-phase diffraction heavily relies on complex ab initio electronic or vibrational excited state simulations to make conclusive interpretations. Without such simulations, inverting this measurement for the structural probability distribution is typically intractable. This creates a so-called inverse problem. In this work, we develop a broadly applicable method that addresses this inverse problem by approximating the molecular frame structure $|Ψ(\boldsymbol{R}, t)|^2$ distribution independent of these complex simulations. We retrieve the vibronic ground state $|Ψ(\boldsymbol{R})|^2$ for both simulated stretched NO$_2$ and measured N$_2$O. From measured N$_2$O, we observe 40 mAngstroms coordinate-space resolution from 3.75 inverse Angstroms reciprocal space range and poor signal-to-noise, a 50X improvement over traditional Fourier transform methods. In simulated NO$_2$, typical to high signal-to-noise levels predict 100--1000X resolution improvements, down to 0.1 mAngstroms. By directly measuring the width of $|Ψ(\boldsymbol{R})|^2$, we open ultrafast gas-phase diffraction capabilities to measurements beyond current analysis approaches. This method has the potential to effectively turn gas-phase ultrafast diffraction into a discovery-oriented technique to probe systems that are prohibitively difficult to simulate.

physics.atom-ph↗

arXiv2023

Investigating dissociation pathways of nitrobenzene via mega-electron-volt ultrafast electron diffraction

As the simplest nitroaromatic compound, nitrobenzene is an interesting model system to explore the rich photochemistry of nitroaromatic compounds. Previous measurements of nitrobenzene's photochemical dynamics have probed structural and electronic properties, which, at times, paint a convoluted and sometimes contradictory description of the photochemical landscape. A sub-picosecond structural probe can complement previous electronic measurements and aid in determining the photochemical dynamics with less ambiguity. We investigate the ultrafast dynamics of nitrobenzene triggered by photoexcitation at 267 nm employing megaelectronvolt ultrafast electron diffraction with femtosecond time resolution. We measure the first 5 ps of dynamics and, by comparing our measured results to simulation, we unambiguously distinguish the lowest singlet and triplet electronic states. We observe ground state recovery within 160 +/- 60 fs through internal conversions and without signal corresponding to photofragmentation. Our lack of dissociation signal within the first 5 ps indicates that previously observed photofragmenation reactions take place in the vibrationally "hot" ground state on timescales considerably beyond 5 ps.

physics.chem-ph↗

arXiv2023

Femtosecond electronic and hydrogen structural dynamics in ammonia imaged with ultrafast electron diffraction

Directly imaging structural dynamics involving hydrogen atoms by ultrafast diffraction methods is complicated by their low scattering cross-sections. Here we demonstrate that megaelectronvolt ultrafast electron diffraction is sufficiently sensitive to follow hydrogen dynamics in isolated molecules. In a study of the photodissociation of gas phase ammonia, we simultaneously observe signatures of the nuclear and corresponding electronic structure changes resulting from the dissociation dynamics in the time-dependent diffraction. Both assignments are confirmed by ab initio simulations of the photochemical dynamics and the resulting diffraction observable. While the temporal resolution of the experiment is insufficient to resolve the dissociation in time, our results represent an important step towards the observation of proton dynamics in real space and time.

physics.chem-ph↗

arXiv2022

Rehybridization dynamics into the pericyclic minimum of an electrcyclic reaction imaged in real-time

Electrocyclic reactions are characterized by the concerted formation and cleavage of both σ and π bonds through a cyclic structure. This structure is known as a pericyclic transition state for thermal reactions and a pericyclic minimum in the excited state for photochemical reactions. However, the structure of the pericyclic geometry has yet to be observed experimentally. We use a combination of ultrafast electron diffraction and excited state wavepacket simulations to image structural dynamics through the pericyclic minimum of a photochemical electrocyclic ring-opening reaction in the molecule α-terpinene. The structural motion into the pericyclic minimum is dominated by rehybridization of two carbon atoms, which is required for the transformation from two to three conjugated π bonds. The σ bond dissociation largely happens after internal conversion from the pericyclic minimum to the electronic ground state. These findings may be transferrable to electrocyclic reactions in general.

physics.chem-ph↗

arXiv2016

Diffractive Imaging of Coherent Nuclear Motion in Isolated Molecules

Observing the motion of the nuclear wavepackets during a molecular reaction, in both space and time, is crucial for understanding and controlling the outcome of photoinduced chemical reactions. We have imaged the motion of a vibrational wavepacket in isolated iodine molecules using ultrafast electron diffraction with relativistic electrons. The time-varying interatomic distance was measured with a precision 0.07 Å and temporal resolution of 230 fs full-width at half-maximum (FWHM). The method is not only sensitive to the position but also the shape of the nuclear wavepacket.

physics.chem-ph↗