arXiv subjects

Andrew S. Lee

Publications and source records attributed to Andrew S. Lee.

3 recordsLinked to original sources

arXiv2026

Tensor learning with orthogonal, Lorentz, and symplectic symmetries

Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address problems in these domains. In this paper, we show how to exploit the underlying symmetries of functions that map tensors to tensors. More concretely, we develop universally expressive equivariant machine learning architectures on tensors that exploit that, in many cases, these tensor functions are equivariant with respect to the diagonal action of the orthogonal, Lorentz, and/or symplectic groups. We showcase our results on three problems coming from material science, theoretical computer science, and time series analysis. For time series, we combine our method with the increasingly popular path signatures approach, which is also invariant with respect to reparameterizations. Our numerical experiments show that our equivariant models perform better than corresponding non-equivariant baselines.

stat.ML↗

arXiv2025

The rigid-flexible value for symplectic embeddings of four-dimensional ellipsoids into polydiscs

We consider the embedding function $c_b(a)$ describing the problem of symplectically embedding an ellipsoid $E(1,a)$ into the smallest scaling of the polydisc $P(1,b)$. Previous work suggests that determining the entirety of $c_b(a)$ for all $b$ is difficult, as infinite staircases can appear for many sequences of irrational $b$. In contrast, we show that for every polydisc $P(1,b)$ with $b>2$, there is an explicit formula for the minimum $a$ such that the embedding problem is determined only by volume. That is, when the ellipsoid is sufficiently stretched, there is a symplectic embedding of $E(1,a)$ fully filling an appropriately scaled polydisc $P(λ,λb)$. Denoted $RF(b)$, this rigid-flexible ($RF$) value is piecewise smooth with a discrete set of discontinuities for $b>2$. At the same time, by exhibiting a sequence of obstructive classes for $b_n = \frac{n+1}{n}$ at $a=8$, we show % that $c_{b_n}(8)$ is above the volume constraint. So, in combination with the Frenkel-Müller result, it follows that $RF$ is also discontinuous at $b=1$.

math.SG↗

arXiv2024

A case study of multi-modal, multi-institutional data management for the combinatorial materials science community

Although the convergence of high-performance computing, automation, and machine learning has significantly altered the materials design timeline, transformative advances in functional materials and acceleration of their design will require addressing the deficiencies that currently exist in materials informatics, particularly a lack of standardized experimental data management. The challenges associated with experimental data management are especially true for combinatorial materials science, where advancements in automation of experimental workflows have produced datasets that are often too large and too complex for human reasoning. The data management challenge is further compounded by the multi-modal and multi-institutional nature of these datasets, as they tend to be distributed across multiple institutions and can vary substantially in format, size, and content. To adequately map a materials design space from such datasets, an ideal materials data infrastructure would contain data and metadata describing i) synthesis and processing conditions, ii) characterization results, and iii) property and performance measurements. Here, we present a case study for the low-barrier development of such a dashboard that enables standardized organization, analysis, and visualization of a large data lake consisting of combinatorial datasets of synthesis and processing conditions, X-ray diffraction patterns, and materials property measurements generated at several different institutions. While this dashboard was developed specifically for data-driven thermoelectric materials discovery, we envision the adaptation of this prototype to other materials applications, and, more ambitiously, future integration into an all-encompassing materials data management infrastructure.

cond-mat.mtrl-sci↗