Related papers: Building maximal green sequences via component pre…
Machine learning has recently emerged as a powerful tool for generating new molecular and material structures. The success of state-of-the-art models stems from their ability to incorporate physical symmetries, such as translation,…
Modern instances of combinatorial optimization problems often exhibit billion-scale ground sets, which have many uninformative or redundant elements. In this work, we develop light-weight pruning algorithms to quickly discard elements that…
We propose generative neural network methods to generate DNA sequences and tune them to have desired properties. We present three approaches: creating synthetic DNA sequences using a generative adversarial network; a DNA-based variant of…
When a neural network can learn multiple distinct algorithms to solve a task, how does it "choose" between them during training? To approach this question, we take inspiration from ecology: when multiple species coexist, they eventually…
We introduce a family of Galerkin finite element methods which are constructed via recovery operators over element-wise discontinuous approximation spaces. This new family, termed collectively as recovered finite element methods (R-FEM) has…
A method for constructing evolution equations admitting a master symmetry is proposed. Several examples illustrating the method are presented. It is also noted that for certain evolution equations master symmetries can be useful for…
We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…
Generative AI has made remarkable progress in addressing various design challenges. One prominent area where generative AI could bring significant value is in engineering design. In particular, selecting an optimal set of components and…
In simulation sciences, it is desirable to capture the real-world problem features as accurately as possible. Methods popular for scientific simulations such as the finite element method (FEM) and finite volume method (FVM) use piecewise…
The persistence barcode is a well-established complete discrete invariant for finitely generated persistence modules [5] [1]. Its definition, however, does not extend to multi- dimensional persistence modules. In this paper, we introduce a…
Recently, diffusion models have achieved significant advances in vision, text, and robotics. However, they still face slow generation speeds due to sequential denoising processes. To address this, a parallel sampling method based on Picard…
Modern clustering approaches often trade interpretability for performance, particularly in deep learning-based methods. We present Generative Kernel Spectral Clustering (GenKSC), a novel model combining kernel spectral clustering with…
A novel particle merging algorithm for rarefied gas dynamics simulations is proposed that can conserve arbitrary velocity and spatial moments of the particle distribution via solving a non-negative least squares problem. An extension that…
Distributed storage systems with replication are well known for storing large amount of data. A large number of replication is done in order to provide reliability. This makes the system expensive. Various methods have been proposed over…
In quantum many-body systems, measurements can induce qualitative new features, but their simulation is hindered by the exponential complexity involved in sampling the measurement results. We propose to use machine learning to assist the…
The unique capability of quantum mechanics to evolve alternative possibilities in parallel is appealing and over the years a number of quantum algorithms have been developed offering great computational benefits. Systems coupled to the…
With recent high-throughput technology we can synthesize large heterogeneous collections of DNA structures, and also read them all out precisely in a single procedure. Can we use these tools, not only to do things faster, but also to devise…
Next-generation sequencing techniques have facilitated a large scale analysis of human genetic variation. Despite the advances in sequencing speeds, the computational discovery of structural variants is not yet standard. It is likely that…
Multi-segment reconstruction (MSR) problem consists of recovering a signal from noisy segments with unknown positions of the observation windows. One example arises in DNA sequence assembly, which is typically solved by matching short reads…
In the second part of this series, we use the Lagrange multiplier approach proposed in the first part \cite{CheS21} to construct efficient and accurate bound and/or mass preserving schemes for a class of semi-linear and quasi-linear…