Publications

This work addresses the question of uniqueness and regularity of the minimizers of a convex but not strictly convex integral functional with linear growth in a two-dimensional setting. The integrand -- whose precise form derives directly from the theory of perfect plasticity -- behaves quadratically close to the origin and grows linearly once a specific threshold is reached. Thus, in contrast with the only existing literature on uniqueness for functionals with linear growth, that is that which pertains to the generalized least gradient, the integrand is not a norm. We make use of hyperbolic conservation laws hidden in the structure of the problem to tackle uniqueness. Our argument strongly relies on the regularity of a vector field -- the Cauchy stress in the terminology of perfect plasticity -- which allows us to define characteristic lines, and then to employ the method of characteristics. Using the detailed structure of the characteristic landscape evidenced in our preliminary study BF, we show that this vector field is actually continuous, save for possibly two points. The different behaviors of the energy density at zero and at infinity imply an inequality constraint on the Cauchy stress. Under a barrier type convexity assumption on the set where the inequality constraint is saturated, we show that uniqueness holds for pure Dirichlet boundary data devoid of any regularity properties, a stronger result than that of uniqueness for a given trace on the whole boundary since our minimizers can fail to attain the boundary data. We also show a partial regularity result for the minimizer.

Due in part to their discontinuous and discrete default encodings for numbers, Large Language Models (LLMs) have not yet been commonly used to process numerically-dense scientific datasets. Rendering datasets as text, however, could help aggregate diverse and multi-modal scientific data into a single training corpus, thereby potentially facilitating the development of foundation models for science. In this work, we introduce xVal, a strategy for continuously tokenizing numbers within language models that results in a more appropriate inductive bias for scientific applications. By training specially-modified language models from scratch on a variety of scientific datasets formatted as text, we find that xVal generally outperforms other common numerical tokenization strategies on metrics including out-of-distribution generalization and computational efficiency.

We introduce multiple physics pretraining (MPP), an autoregressive task-agnostic pretraining approach for physical surrogate modeling of spatiotemporal systems with transformers. In MPP, rather than training one model on a specific physical system, we train a backbone model to predict the dynamics of multiple heterogeneous physical systems simultaneously in order to learn features that are broadly useful across systems and facilitate transfer. In order to learn effectively in this setting, we introduce a shared embedding and normalization strategy that projects the fields of multiple systems into a shared embedding space. We validate the efficacy of our approach on both pretraining and downstream tasks over a broad fluid mechanics-oriented benchmark. We show that a single MPP-pretrained transformer is able to match or outperform task-specific baselines on all pretraining sub-tasks without the need for finetuning. For downstream tasks, we demonstrate that finetuning MPP-trained models results in more accurate predictions across multiple time-steps on systems with previously unseen physical components or higher dimensional systems compared to training from scratch or finetuning pretrained video foundation models. We open-source our code and model weights trained at multiple scales for reproducibility.

We introduce an efficient numerical method for second-order linear ODEs whose solution may vary between highly oscillatory and slowly changing over the solution interval. In oscillatory regions the solution is generated via a nonoscillatory phase function that obeys the nonlinear Riccati equation. We propose a defect correction iteration that gives an asymptotic series for such a phase function; this is numerically approximated on a Chebyshev grid with a small number of nodes. For analytic coefficients we prove that each iteration, up to a certain maximum number, reduces the residual by a factor of order of the local frequency. The algorithm adapts both the stepsize and the choice of method, switching to a conventional spectral collocation method away from oscillatory regions. In numerical experiments we find that our proposal outperforms other state-of-the-art oscillatory solvers, most significantly at low to intermediate frequencies and at low tolerances, where it may use up to $10^6$ times fewer function evaluations. Even in high-frequency regimes, our implementation is on average 10 times faster than other specialized solvers.

TGF-β, essential for development and immunity, is expressed as a latent complex (L-TGF-β) non-covalently associated with its prodomain and presented on immune cell surfaces by covalent association with GARP. Binding to integrin αvβ8 activates L-TGF-β1/GARP. The dogma is that mature TGF-β must physically dissociate from L-TGF-β1 for signaling to occur. Our previous studies discovered that αvβ8-mediated TGF-β autocrine signaling can occur without TGF-β1 release from its latent form. Here, we show that mice engineered to express TGF-β1 that cannot release from L-TGF-β1 survive without early lethal tissue inflammation, unlike those with TGF-β1 deficiency. Combining cryogenic electron microscopy with cell-based assays, we reveal a dynamic allosteric mechanism of autocrine TGF-β1 signaling without release where αvβ8 binding redistributes the intrinsic flexibility of L-TGF-β1 to expose TGF-β1 to its receptors. Dynamic allostery explains the TGF-β3 latency/activation mechanism and why TGF-β3 functions distinctly from TGF-β1, suggesting that it broadly applies to other flexible cell surface receptor/ligand systems.

We introduce cppdlr, a C++ library implementing the discrete Lehmann representation (DLR) of functions in imaginary time and Matsubara frequency, such as Green's functions and self-energies. The DLR is based on a low-rank approximation of the analytic continuation kernel, and yields a compact and explicit basis consisting of exponentials in imaginary time and simple poles in Matsubara frequency. cppdlr constructs the DLR basis and associated interpolation grids, and implements standard operations. It provides a flexible yet high-level interface, facilitating the incorporation of the DLR into both small-scale applications and existing large-scale software projects.

Extracting consistent statistics between relevant free energy minima of a molecular system is essential for physics, chemistry, and biology. Molecular dynamics (MD) simulations can aid in this task but are computationally expensive, especially for systems that require quantum accuracy. To overcome this challenge, we developed an approach combining enhanced sampling with deep generative models and active learning of a machine learning potential (MLP). We introduce an adaptive Markov chain Monte Carlo framework that enables the training of one normalizing flow (NF) and one MLP per state, achieving rapid convergence toward the Boltzmann distribution. Leveraging the trained NF and MLP models, we compute thermodynamic observables such as free energy differences and optical spectra. We apply this method to study the isomerization of an ultrasmall silver nanocluster belonging to a set of systems with diverse applications in the fields of medicine and catalysis.

We consider the analysis of singular waveguides separating insulating phases in two-space dimensions. The insulating domains are modeled by a massive Schrödinger equation and the singular waveguide by appropriate jump conditions along the one-dimensional interface separating the insulators. We present an integral formulation of the problem and analyze its mathematical properties. We also implement a fast multipole and sweeping-accelerated iterative algorithm for solving the integral equations, and demonstrate numerically the fast convergence of this method. Several numerical examples of solutions and scattering effects illustrate our theory.

2D template matching (2DTM) can be used to detect molecules and their assemblies in cellular cryo-EM images with high positional and orientational accuracy. While 2DTM successfully detects spherical targets such as large ribosomal subunits, challenges remain in detecting smaller and more aspherical targets in various environments. In this work, a novel 2DTM metric, referred to as the 2DTM p-value, is developed to extend the 2DTM framework to more complex applications. The 2DTM p-value combines information from two previously used 2DTM metrics, namely the 2DTM signal-to-noise ratio (SNR) and z-score, which are derived from the cross-correlation coefficient between the target and the template. The 2DTM p-value demonstrates robust detection accuracies under various imaging and sample conditions and outperforms the 2DTM SNR and z-score alone. Specifically, the 2DTM p-value improves the detection of aspherical targets such as a modified artificial tubulin patch particle (500 kDa) and a much smaller clathrin monomer (193 kDa) in simulated data. It also accurately recovers mature 60S ribosomes in yeast lamellae samples, even under conditions of increased Gaussian noise. The new metric will enable the detection of a wider variety of targets in both purified and cellular samples through 2DTM.

We augment the `QUAsi-symmetric Stellarator Repository' (QUASR) to include vacuum field stellarators with quasihelical symmetry using a globalized optimization workflow. The database now has almost 370,000 quasisaxisymmetry and quasihelically symmetric devices along with coil sets, optimized for a variety of aspect ratios, rotational transforms, and discrete rotational symmetries. This paper outlines a couple of ways to explore and characterize the data set. We plot devices on a near-axis quasisymmetry landscape, revealing close correspondence to this predicted landscape. We also use principal component analysis to reduce the dimensionality of the data so that it can easily be visualized in two or three dimensions. Principal component analysis also gives a mechanism to compare the new devices here to previously published ones in the literature. We are able to characterize the structure of the data, observe clusters, and visualize the progression of devices in these clusters. These techniques reveal that the data has structure, and that typically one, two or three principal components are sufficient to characterize it. QUASR is archived at this https URL and can be explored online at this http URL.