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Ronan Le Bras

Publications and source records attributed to Ronan Le Bras.

58 records · Page 4Linked to original sources

Automated Phase Mapping with AgileFD and its Application to Light Absorber Discovery in the V-Mn-Nb Oxide System

Rapid construction of phase diagrams is a central tenet of combinatorial materials science with accelerated materials discovery efforts often hampered by challenges in interpreting combinatorial x-ray diffraction datasets, which we address by developing AgileFD, an artificial intelligence algorithm that enables rapid phase mapping from a combinatorial library of x-ray diffraction patterns. AgileFD models alloying-based peak shifting through a novel expansion of convolutional nonnegative matrix factorization, which not only improves the identification of constituent phases but also maps their concentration and lattice parameter as a function of composition. By incorporating Gibbs phase rule into the algorithm, physically meaningful phase maps are obtained with unsupervised operation, and more refined solutions are attained by injecting expert knowledge of the system. The algorithm is demonstrated through investigation of the V-Mn-Nb oxide system where decomposition of eight oxide phases, including two with substantial alloying, provides the first phase map for this pseudo-ternary system. This phase map enables interpretation of high-throughput band gap data, leading to the discovery of new solar light absorbers and the alloying-based tuning of the direct-allowed band-gap energy of MnV2O6. The open-source family of AgileFD algorithms can be implemented into a broad range of high throughput workflows to accelerate materials discovery.

cond-mat.mtrl-sci↗

Variable Elimination in the Fourier Domain

The ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major computational advantages. We explore a different type of compact representation based on discrete Fourier representations, complementing the classical approach based on conditional independencies. We show that a large class of probabilistic graphical models have a compact Fourier representation. This theoretical result opens up an entirely new way of approximating a probability distribution. We demonstrate the significance of this approach by applying it to the variable elimination algorithm. Compared with the traditional bucket representation and other approximate inference algorithms, we obtain significant improvements.

cs.AI↗

Pattern Decomposition with Complex Combinatorial Constraints: Application to Materials Discovery

Identifying important components or factors in large amounts of noisy data is a key problem in machine learning and data mining. Motivated by a pattern decomposition problem in materials discovery, aimed at discovering new materials for renewable energy, e.g. for fuel and solar cells, we introduce CombiFD, a framework for factor based pattern decomposition that allows the incorporation of a-priori knowledge as constraints, including complex combinatorial constraints. In addition, we propose a new pattern decomposition algorithm, called AMIQO, based on solving a sequence of (mixed-integer) quadratic programs. Our approach considerably outperforms the state of the art on the materials discovery problem, scaling to larger datasets and recovering more precise and physically meaningful decompositions. We also show the effectiveness of our approach for enforcing background knowledge on other application domains.

cs.AI↗

On the Erdos Discrepancy Problem

According to the Erdős discrepancy conjecture, for any infinite $\pm 1$ sequence, there exists a homogeneous arithmetic progression of unbounded discrepancy. In other words, for any $\pm 1$ sequence $(x_1,x_2,...)$ and a discrepancy $C$, there exist integers $m$ and $d$ such that $|\sum_{i=1}^m x_{i \cdot d}| > C$. This is an $80$-year-old open problem and recent development proved that this conjecture is true for discrepancies up to $2$. Paul Erdős also conjectured that this property of unbounded discrepancy even holds for the restricted case of completely multiplicative sequences (CMSs), namely sequences $(x_1,x_2,...)$ where $x_{a \cdot b} = x_{a} \cdot x_{b}$ for any $a,b \geq 1$. The longest CMS with discrepancy $2$ has been proven to be of size $246$. In this paper, we prove that any completely multiplicative sequence of size $127,646$ or more has discrepancy at least $4$, proving the Erdős discrepancy conjecture for CMSs of discrepancies up to $3$. In addition, we prove that this bound is tight and increases the size of the longest known sequence of discrepancy $3$ from $17,000$ to $127,645$. Finally, we provide inductive construction rules as well as streamlining methods to improve the lower bounds for sequences of higher discrepancies.

cs.DM↗