Related papers: Machine Learning the Dimension of a Polytope
A machine learning approach is presented to accelerate the computation of block polymer morphology evolution for large domains over long timescales. The strategy exploits the separation of characteristic times between coarse-grained…
In the presence of strong electronic spin correlations, the hyperfine interaction imparts long-range coupling between nuclear spins. Efficient protocols for the extraction of such complex information about electron correlations via magnetic…
We introduce LOT Wassmap, a computationally feasible algorithm to uncover low-dimensional structures in the Wasserstein space. The algorithm is motivated by the observation that many datasets are naturally interpreted as probability…
We describe a recursive algorithm that decomposes an algebraic set into locally closed equidimensional sets, i.e. sets which each have irreducible components of the same dimension. At the core of this algorithm, we combine ideas from the…
Machine learning pipelines that include a combinatorial optimization layer can give surprisingly efficient heuristics for difficult combinatorial optimization problems. Three questions remain open: which architecture should be used, how…
Metric magnitude is a measure of the "size" of point clouds with many desirable geometric properties. It has been adapted to various mathematical contexts and recent work suggests that it can enhance machine learning and optimization…
A multi-layer perceptron neural network was used to predict the laser transition figure of merit, a measure of the laser threshold gain, of over 900 million Quantum Cascade Laser designs using only layer thicknesses and the applied electric…
The accurate and precise extraction of information from a modern particle physics detector, such as an electromagnetic calorimeter, may be complicated and challenging. In order to overcome the difficulties we propose processing the detector…
In this paper we use neural networks to learn governing equations from data. Specifically we reconstruct the right-hand side of a system of ODEs $\dot{x}(t) = f(t, x(t))$ directly from observed uniformly time-sampled data using a neural…
We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…
Computing the volume of a polytope in high dimensions is computationally challenging but has wide applications. Current state-of-the-art algorithms to compute such volumes rely on efficient sampling of a Gaussian distribution restricted to…
We consider computer generated configurations of quantised vortices in planar superfluid Bose-Einstein condensates. We show that unsupervised machine learning technology can successfully be used for classifying such vortex configurations to…
Developing deterministic neighborhood-informed point-particle closure models using machine learning has garnered interest in recent times from dispersed multiphase flow community. The robustness of neural models for this complex multi-body…
In this talk we discuss a novel method, that we have presented in Ref. [1], to extract hadronic spectral densities from lattice correlators by using deep learning techniques. Hadronic spectral densities play a crucial role in the study of…
The neutrino closure method is often used to obtain kinematics of semileptonic decays with one unreconstructed particle. The kinematics of decays can be deducted by a two-fold ambiguity with a quadratic equation. To resolve the two-fold…
In this paper, we evaluate the accuracy of deep learning approaches on geospatial vector geometry classification tasks. The purpose of this evaluation is to investigate the ability of deep learning models to learn from geometry coordinates…
We study the computational complexity of determining the Hausdorff distance of two polytopes given in halfspace- or vertex-presentation in arbitrary dimension. Subsequently, a matching problem is investigated where a convex body is allowed…
In this work we explore the application of deep neural networks to the optimization of atomic layer deposition processes based on thickness values obtained at different points of an ALD reactor. We introduce a dataset designed to train…
We utilize extreme-learning machines for the prediction of partial differential equations (PDEs). Our method splits the state space into multiple windows that are predicted individually using a single model. Despite requiring only few data…
A seminal result of E. Ehrhart states that the number of integer lattice points in the dilation of a rational polytope by a positive integer $k$ is a quasi-polynomial function of $k$ --- that is, a "polynomial" in which the coefficients are…