Related papers: On the basis-set extrapolation
We investigate the existence of well-behaved Beurling number systems, which are systems of Beurling generalized primes and integers which admit a power saving in the error term of both their prime and integer-counting function. Concretely,…
We study the problem of list ranking in the parallel external memory (PEM) model. We observe an interesting dual nature for the hardness of the problem due to limited information exchange among the processors about the structure of the…
This paper proposes a novel computationally efficient algorithm for optimal sizing of Battery Energy Storage Systems (BESS) considering renewable energy bidding strategies. Unlike existing two-stage methods, our algorithm enables the…
Fixed-parameter algorithms, approximation algorithms and moderately exponential algorithms are three major approaches to algorithms design. While each of them being very active in its own, there is an increasing attention to the connection…
This paper describes a very efficient algorithm for image signal extrapolation. It can be used for various applications in image and video communication, e.g. the concealment of data corrupted by transmission errors or prediction in video…
We present a simple linear model to estimate the basis set incompleteness errors (BSIE) of (vertex-corrected) $GW$ QP energies based on the kinetic energy of the corresponding orbital only. We parametrise the model for $G_0W_0$,…
Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foundation model for scientific problems, named PROSE-PDE. Our…
We investigate the endofullerene system $^3$He@C$_{60}$ with a four-dimensional Potential Energy Surface (PES) to include the three He translational degrees of freedom and C$_{60}$ cage radius. We compare MP2, SCS-MP2, SOS-MP2, RPA@PBE and…
Efficient solvers for tensor eigenvalue problems are important tools for the analysis of higher-order data sets. Here we introduce, analyze and demonstrate an extrapolation method to accelerate the widely used shifted symmetric higher order…
A subroutine for very-high-precision numerical solution of a class of ordinary differential equations is provided. For given evaluation point and equation parameters the memory requirement scales linearly with precision $P$, and the number…
Sequences of experimental ground-state energies are mapped onto concave patterns cured from convexities due to pairing and/or shell effects. The same patterns, completed by a list of excitation energies, can be used to give numerical…
We introduce BEDS (Bayesian Emergent Dissipative Structures), a formal framework for analyzing inference systems that must maintain beliefs continuously under energy constraints. Unlike classical computational models that assume perfect…
Continual learning (CL) has traditionally focused on minimizing exemplar memory, a constraint often misaligned with modern systems where GPU time, not storage, is the primary bottleneck. This paper challenges this paradigm by investigating…
We present an approach that extends the theory of targeted free energy perturbation (TFEP) to calculate free energy differences and free energy surfaces at an accurate quantum mechanical level of theory from a cheaper reference potential.…
In dealing with high-dimensional data, factor models are often used for reducing dimensions and extracting relevant information. The spectrum of covariance matrices from power data exhibits two aspects: 1) bulk, which arises from random…
Approximate algorithms for structured prediction problems---such as LP relaxations and the popular alpha-expansion algorithm (Boykov et al. 2001)---typically far exceed their theoretical performance guarantees on real-world instances. These…
An approach to the extraction of the two-photon exchange (TPE) correction from elastic $ep$ scattering data is presented. The cross section, polarization transfer (PT), and charge asymmetry data are considered. It is assumed that the TPE…
Recent neural network models for algorithmic tasks have led to significant improvements in extrapolation to sequences much longer than training, but it remains an outstanding problem that the performance still degrades for very long or…
In the era of big data, methods for improving memory and computational efficiency have become crucial for successful deployment of technologies. Hashing is one of the most effective approaches to deal with computational limitations that…
Human can extrapolate well, generalize daily knowledge into unseen scenarios, raise and answer counterfactual questions. To imitate this ability via generative models, previous works have extensively studied explicitly encoding Structural…