Publications

Simulating the dynamics of charged particles in quasi-two-dimensional (quasi-2D) nanoconfined systems presents a significant computational challenge due to the long-range nature of electrostatic interactions and the geometric anisotropy. To address this, we introduce a novel quasi-Ewald splitting strategy tailored for particle-based simulations in such geometry. Our splitting strategy seamlessly integrates a collection of advanced numerical techniques, including optimal quadrature rules [L. N. Trefethen, SIAM Rev. 64(1)(2022), pp.132-150], fast pairwise kernel summation methods [S. Jiang and L. Greengard, Commun. Comput. Phys. 31(1)(2022), pp.1-26], and the random batch method with importance sampling in k-space [S. Jin, L. Li, Z. Xu et al., SIAM J. Sci. Comput. 43(4)(2021), pp.B937-B960]. The resulting algorithm achieves an O(N) overall computational complexity, where N denotes the total number of confined particles. Simulations of several prototype systems validate the accuracy and efficiency of our method. Furthermore, we present numerical observations specifically related to nanoconfined charged many-body systems, highlighting phenomena such as dielectric boundary effects, anisotropic diffusion, and the structure of the electrical double layer (EDL) under conditions of charge asymmetry.

We present an NPT extension of Ewald summation with prolates (ESP), a spectrally accurate and scalable particle-mesh method for molecular dynamics simulations of periodic, charged systems. Building on the recently introduced ESP framework, this work focuses on rigorous and thermodynamically consistent pressure/stress evaluation in the isothermal--isobaric ensemble. ESP employs prolate spheroidal wave functions as both splitting and spreading kernels, reducing the Fourier grid size needed to reach a prescribed pressure accuracy compared with current widely used mesh-Ewald methods based on Gaussian splitting and B-spline spreading. We derive a unified pressure-tensor formulation applicable to isotropic, semi-isotropic, anisotropic, and fully flexible cells, and show that the long-range pressure can be evaluated with a single forward FFT followed by diagonal scaling, whereas force evaluation requires both forward and inverse transforms. We provide production implementations in LAMMPS and GROMACS and validate pressure and force accuracy on bulk water, LiTFSI ionic liquids, and a transmembrane system. Benchmarks on up to 3×103 CPU cores demonstrate strong scaling and reduced communication cost at matched accuracy, particularly for NPT pressure evaluation.

Cryogenic electron microscopy (cryo-EM) has emerged as a powerful method for resolving the structure of biological macromolecules. Recently, several computational methods have been developed to study the heterogeneity of molecules in single-particle cryo-EM. In this study, we analyze a publicly available dataset of TRPV1 using five such methods: 3DFlex, 3DVA, cryoDRGN, ManifoldEM, and Bayesian ensemble reweighting. We find significant heterogeneity, but each method produces different results, with some detecting only compositional or conformational heterogeneity. To compare these diverse results, we develop AnaVox to quantitatively determine agreement between heterogeneity methods. Furthermore, applying Bayesian ensemble reweighting combined with molecular dynamics simulations supports the presence of these rarer states within the sample. This study shows that although current methods reveal the presence of heterogeneity, their stochasticity and potential bias present challenges for their routine use. However, with future development, these tools will enable the use of cryo-EM data for quantitative biophysical investigations.

Many tasks in single-particle cryo-electron microscopy (cryo-EM), such as 2D/3D classification and homo/heterogeneous reconstruction, require optimizing model parameters to minimize the discrepancy between observed data and a forward model. The standard Mean Squared Error (MSE) loss function is computationally efficient but suffers from a non-convex rugged loss landscape, particularly for high-resolution heterogeneity inference. In this work, we investigate the practical utility of Sliced Wasserstein (SW) distances. We implement exact W2 estimators (inverse-CDF and greedy matching) of projections alongside a computationally efficient proxy based on the L2 norm of CDFs, a formulation akin to the sliced Cramér–von Mises distance. We establish the latter as a robust, fully differentiable workhorse for the cryo-EM forward model. We evaluate its performance against the MSE in joint inference tasks recovering pose, CTF parameters, and conformational heterogeneity. Our results demonstrate that SW significantly broadens the basin of attraction, enabling robust gradient-based optimization from distant initializations where MSE fails. Using a helical spiral toy model, we highlight how SW losses are sensitive to per-particle contrast, where background noise level miscalibration can induce geometric bias in the inferred structure. We show that this bias is manageable through a joint optimization strategy that treats background contrast as a learnable parameter. Finally, we validate the approach on a synthetic dataset using the Zernike3D framework, showing that the SW loss works and yields an accurate landscape representations, comparable with MSE. These findings establish SW as a powerful tool for navigating the rugged landscapes of cryo-EM forward model parameters

Singularity swap quadrature (SSQ) is an effective method for the evaluation at nearby targets of potentials due to densities on curves in three dimensions. While highly accurate in most settings, it is known to suffer from catastrophic cancellation when the kernel exhibits both near-vanishing numerators and strong singularities, as arises with scalar double layer potentials or tensorial kernels in Stokes flow or linear elasticity. This precision loss turns out to be tied to the interpolation basis, namely monomial (for open curves) or Fourier (for closed curves). We introduce a simple yet powerful remedy: target-specific translated monomial and Fourier bases that explicitly incorporate the near-vanishing behavior of the kernel numerator. We combine this with a stable evaluation of the constant term which now dominates the integral, significantly reducing cancellation. We show that our approach achieves close to machine precision for prototype integrals, and up to ten orders of magnitude lower error than standard SSQ at extremely close evaluation distances, without significant additional computational cost.

The DANDI Archive is a key resource for sharing open neurophysiology data, hosting over 400 datasets in the Neurodata Without Borders (NWB) format. While these datasets hold tremendous potential for reanalysis and discovery, many researchers face barriers to reuse, including unfamiliarity with access methods and difficulty identifying relevant content. Here we introduce an AI-powered, agentic chat assistant and a notebook generation pipeline. The chat assistant serves as an interactive tool for exploring DANDI datasets. It leverages large language models (LLMs) and integrates with agentic tools to guide users through data access, visualization, and preliminary analysis. The notebook generator analyzes dataset structure with minimal human input, executing inspection scripts and generating visualizations. It then produces an instructional Python notebook tailored to the dataset. We applied this system to 12 recent datasets. Review by neurophysiology data specialists found the generated notebooks to be generally accurate and well-structured, with most notebooks rated as “very helpful.” This work demonstrates how AI can support FAIR principles by leveraging data standards and lowering barriers to data reuse and engagement.

Although the Kadanoff-Baym equations are typically solved using time-stepping methods, iterative global-in-time solvers offer potential algorithmic advantages, particularly when combined with compressed representations of two-time objects. We examine the computational complexity and stability of several global-in-time iterative methods, including multiple variants of fixed point iteration, Jacobian-free methods, and a Newton-Krylov method using automatic differentiation. We consider the ramped and periodically-driven Falicov-Kimball and Hubbard models within time-dependent dynamical mean-field theory. Although we observe that several iterative methods yield stable convergence at large propagation times, a standard forward fixed point iteration does not. We find that the number of iterations required to converge to a given accuracy with a fixed time step size scales roughly linearly with the number of time steps. This scaling is associated with the formation of a propagating front in the residual error, whose velocity is method-dependent. We identify key challenges which must be addressed in order to make global solvers competitive with time-stepping methods.

Inverse medium scattering is an ill-posed, nonlinear wave-based imaging problem arising in medical imaging, remote sensing, and non-destructive testing. Machine learning (ML) methods offer increased inference speed and flexibility in capturing prior knowledge of imaging targets relative to classical optimization-based approaches; however, they perform poorly in regimes where the scattering behavior is highly nonlinear. A key limitation is that ML methods struggle to incorporate the physics governing the scattering process, which are typically inferred implicitly from the training data or loosely enforced via architectural design. In this paper, we present a method that endows a machine learning framework with explicit knowledge of problem physics, in the form of a differentiable solver representing the forward model. The proposed method progressively refines reconstructions of the scattering potential using measurements at increasing wave frequencies, following a classical strategy to stabilize recovery. Empirically, we find that our method provides high-quality reconstructions at a fraction of the computational or sampling costs of competing approaches.

Large language models (LLMs) are increasingly capable of emulating reasoning and using tools, creating opportunities for autonomous agents that execute complex scientific tasks. Protein design provides a natural case study: existing deep learning models achieve strong results, but they are typically restricted to canonical amino acids and narrow objectives, leaving space for a generalist tool for broad design pipelines. We introduce Agent Rosetta, an LLM agent built on top of the Rosetta suite---the leading physics-based software for heteropolymer design, capable of modeling non-canonical building blocks and geometries. Agent Rosetta is a single-agent, multi-turn framework that iteratively refines heteropolymers to achieve the goals of a user-defined task brief, combining the biophysical knowledge of modern LLMs with the accuracy of Rosetta's physics-based methods. In evaluations, Agent Rosetta achieves performance comparable to specialized deep learning models, especially when combined with inference-time techniques such as best-of-n sampling. Interestingly, we find that prompt engineering alone is insufficient for reliably producing RosettaScripts actions. This underscores the need for building a comprehensive environment that, for example, simplifies the most challenging aspects of RosettaScripts syntax. These results demonstrate that combining frontier LLMs with established domain-specific scientific tools can yield flexible agentic frameworks that not only lower barriers to use but also achieve performance competitive with specialized deep learning models.

Transformers can implement both generalizable algorithms (e.g., induction heads) and simple positional shortcuts (e.g., memorizing fixed output positions). In this work, we study how the choice of pretraining data distribution steers a shallow transformer toward one behavior or the other. Focusing on a minimal trigger-output prediction task -- copying the token immediately following a special trigger upon its second occurrence -- we present a rigorous analysis of gradient-based training of a single-layer transformer. In both the infinite and finite sample regimes, we prove a transition in the learned mechanism: if input sequences exhibit sufficient diversity, measured by a low “max-sum” ratio of trigger-to-trigger distances, the trained model implements an induction head and generalizes to unseen contexts; by contrast, when this ratio is large, the model resorts to a positional shortcut and fails to generalize out-of-distribution (OOD). We also reveal a trade-off between the pretraining context length and OOD generalization, and derive the optimal pretraining distribution that minimizes computational cost per sample. Finally, we validate our theoretical predictions with controlled synthetic experiments, demonstrating that broadening context distributions robustly induces induction heads and enables OOD generalization. Our results shed light on the algorithmic biases of pretrained transformers and offer conceptual guidelines for data-driven control of their learned behaviors.