Tensor Methods: A Unified and Interpretable Approach for Material Design

• URL: http://arxiv.org/abs/2602.10392v1
• Date: Wed, 11 Feb 2026 00:30:39 GMT
• Title: Tensor Methods: A Unified and Interpretable Approach for Material Design
• Authors: Shaan Pakala, Aldair E. Gongora, Brian Giera, Evangelos E. Papalexakis,
• Abstract summary: We suggest the use of tensor completion methods as an all-in-one approach for interpretability and predictions.<n>We study the effects of both types of surrogate models when we encounter training data from a non-uniform sampling of the design space.<n>We find the best generalization comes from a tensor model, which is able to improve upon the baseline ML methods by up to 5% on aggregate $R2$, and halve the error in some out of distribution regions.
• Score: 2.629069307455598
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: When designing new materials, it is often necessary to tailor the material design (with respect to its design parameters) to have some desired properties (e.g. Young's modulus). As the set of design parameters grow, the search space grows exponentially, making the actual synthesis and evaluation of all material combinations virtually impossible. Even using traditional computational methods such as Finite Element Analysis becomes too computationally heavy to search the design space. Recent methods use machine learning (ML) surrogate models to more efficiently determine optimal material designs; unfortunately, these methods often (i) are notoriously difficult to interpret and (ii) under perform when the training data comes from a non-uniform sampling of the design space. We suggest the use of tensor completion methods as an all-in-one approach for interpretability and predictions. We observe classical tensor methods are able to compete with traditional ML in predictions, with the added benefit of their interpretable tensor factors (which are given completely for free, as a result of the prediction). In our experiments, we are able to rediscover physical phenomena via the tensor factors, indicating that our predictions are aligned with the true underlying physics of the problem. This also means these tensor factors could be used by experimentalists to identify potentially novel patterns, given we are able to rediscover existing ones. We also study the effects of both types of surrogate models when we encounter training data from a non-uniform sampling of the design space. We observe more specialized tensor methods that can give better generalization in these non-uniforms sampling scenarios. We find the best generalization comes from a tensor model, which is able to improve upon the baseline ML methods by up to 5% on aggregate $R^2$, and halve the error in some out of distribution regions.

Related papers

• Surrogate Modeling for the Design of Optimal Lattice Structures using Tensor Completion [2.629069307455598]
  We focus on the design of optimal lattice structures with regard to mechanical performance.<n>In this work, we suggest the use of tensor completion as a surrogate model to accelerate the design of materials.
  arXiv  Detail & Related papers  (2025-10-08T19:20:59Z)
• Score-Based Model for Low-Rank Tensor Recovery [49.158601255093416]
  Low-rank tensor decompositions (TDs) provide an effective framework for multiway data analysis.<n>Traditional TD methods rely on predefined structural assumptions, such as CP or Tucker decompositions.<n>We propose a score-based model that eliminates the need for predefined structural or distributional assumptions.
  arXiv  Detail & Related papers  (2025-06-27T15:05:37Z)
• Causal Estimation of Memorisation Profiles [58.20086589761273]
  Understanding memorisation in language models has practical and societal implications. Memorisation is the causal effect of training with an instance on the model's ability to predict that instance. This paper proposes a new, principled, and efficient method to estimate memorisation based on the difference-in-differences design from econometrics.
  arXiv  Detail & Related papers  (2024-06-06T17:59:09Z)
• Scaling and renormalization in high-dimensional regression [72.59731158970894]
  We present a unifying perspective on recent results on ridge regression.<n>We use the basic tools of random matrix theory and free probability, aimed at readers with backgrounds in physics and deep learning.<n>Our results extend and provide a unifying perspective on earlier models of scaling laws.
  arXiv  Detail & Related papers  (2024-05-01T15:59:00Z)
• A Lightweight Generative Model for Interpretable Subject-level Prediction [0.07989135005592125]
  We propose a technique for single-subject prediction that is inherently interpretable. Experiments demonstrate that the resulting model can be efficiently inverted to make accurate subject-level predictions.
  arXiv  Detail & Related papers  (2023-06-19T18:20:29Z)
• Explainability as statistical inference [29.74336283497203]
  We propose a general deep probabilistic model designed to produce interpretable predictions. The model parameters can be learned via maximum likelihood, and the method can be adapted to any predictor network architecture. We show experimentally that using multiple imputation provides more reasonable interpretations.
  arXiv  Detail & Related papers  (2022-12-06T16:55:10Z)
• Visual design intuition: Predicting dynamic properties of beams from raw cross-section images [6.76432840291023]
  We aim to mimic the human ability to acquire the intuition to estimate the performance of a design from visual inspection and experience alone. We study the ability of convolutional neural networks to predict static and dynamic properties of cantilever beams directly from their raw cross-section images.
  arXiv  Detail & Related papers  (2021-11-14T03:10:15Z)
• Equivariant vector field network for many-body system modeling [65.22203086172019]
  Equivariant Vector Field Network (EVFN) is built on a novel equivariant basis and the associated scalarization and vectorization layers. We evaluate our method on predicting trajectories of simulated Newton mechanics systems with both full and partially observed data.
  arXiv  Detail & Related papers  (2021-10-26T14:26:25Z)
• Goal-directed Generation of Discrete Structures with Conditional Generative Models [85.51463588099556]
  We introduce a novel approach to directly optimize a reinforcement learning objective, maximizing an expected reward. We test our methodology on two tasks: generating molecules with user-defined properties and identifying short python expressions which evaluate to a given target value.
  arXiv  Detail & Related papers  (2020-10-05T20:03:13Z)
• Surrogate Locally-Interpretable Models with Supervised Machine Learning Algorithms [8.949704905866888]
  Supervised Machine Learning algorithms have become popular in recent years due to their superior predictive performance over traditional statistical methods. The main focus is on interpretability, the resulting surrogate model also has reasonably good predictive performance.
  arXiv  Detail & Related papers  (2020-07-28T23:46:16Z)
• Good Classifiers are Abundant in the Interpolating Regime [64.72044662855612]
  We develop a methodology to compute precisely the full distribution of test errors among interpolating classifiers. We find that test errors tend to concentrate around a small typical value $varepsilon*$, which deviates substantially from the test error of worst-case interpolating model. Our results show that the usual style of analysis in statistical learning theory may not be fine-grained enough to capture the good generalization performance observed in practice.
  arXiv  Detail & Related papers  (2020-06-22T21:12:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.