相关论文: Inverse Primitive Path Analysis

Composite materials often exhibit mechanical anisotropy owing to the material properties or geometrical configurations of the microstructure. This makes their inverse design a two-fold problem. First, we must learn the type and orientation…

Parallel tempering (PT) is a class of Markov chain Monte Carlo algorithms that constructs a path of distributions annealing between a tractable reference and an intractable target, and then interchanges states along the path to improve…

The Mapper algorithm is an essential tool for visualizing complex, high dimensional data in topology data analysis (TDA) and has been widely used in biomedical research. It outputs a combinatorial graph whose structure implies the shape of…

The inverse problem method is tested for a class of monomer-dimer statistical mechanics models that contain also an attractive potential and display a mean-field critical point at a boundary of a coexistence line. The inversion is obtained…

The complexity class PPA consists of NP-search problems which are reducible to the parity principle in undirected graphs. It contains a wide variety of interesting problems from graph theory, combinatorics, algebra and number theory, but…

Unsupervised learning makes manifest the underlying structure of data without curated training and specific problem definitions. However, the inference of relationships between data points is frustrated by the `curse of dimensionality' in…

Synthetic polymers are versatile and widely used materials. Similar to small organic molecules, a large chemical space of such materials is hypothetically accessible. Computational property prediction and virtual screening can accelerate…

We study the basic problem of robust subspace recovery. That is, we assume a data set that some of its points are sampled around a fixed subspace and the rest of them are spread in the whole ambient space, and we aim to recover the fixed…

Inverse problems describe the task of recovering an underlying signal of interest given observables. Typically, the observables are related via some non-linear forward model applied to the underlying unknown signal. Inverting the non-linear…

The multiscale entanglement renormalization ansatz (MERA) provides a constructive algorithm for realizing wavefunctions that are inherently scale invariant. Unlike conformally invariant partition functions however, the finite bond dimension…

Interpreting spectropolarimetric observations of the solar atmosphere takes much longer than the acquiring the data. The most important reason for this is that the model fitting, or "inversion", used to infer physical quantities from the…

Recently, there has been an explosion in statistical learning literature to represent data using topological principles to capture structure and relationships. We propose a topological data analysis (TDA)-based framework, named Topological…

A path integral reduction procedure in Wiener-type path integrals, based on the approach developed in arXiv:1912.13124, is applied to a simple invariant mechanical system defined on a product manifold with a given free, proper and isometric…

We propose a new method for robust PCA -- the task of recovering a low-rank matrix from sparse corruptions that are of unknown value and support. Our method involves alternating between projecting appropriate residuals onto the set of…

In solid mechanics, Data-driven approaches are widely considered as the new paradigm that can overcome the classic problems of constitutive models such as limiting hypothesis, complexity, and high dependence on training data. However,…

We introduce a neural network architecture to solve inverse problems linked to a one-dimensional integral operator. This architecture is built by unfolding a forward-backward algorithm derived from the minimization of an objective function…

Antimicrobial resistance is one of the biggest health problem, especially in the current period of COVID-19 pandemic. Due to the unique membrane-destruction bactericidal mechanism, antimicrobial peptide-mimetic copolymers are paid more…

Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent…

Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…

How can we design neural networks that allow for stable universal approximation of maps between topologically interesting manifolds? The answer is with a coordinate projection. Neural networks based on topological data analysis (TDA) use…