arXiv research

A GPU-based workflow for building physics emulators of hypersonic flows

RSmote improves PINNs accuracy with less memory usage.

We improve optimization for data with varying variance.

Proposes a neural network method to correct residual distortions in coordinate transformations.

In this paper, we consider a framework adapting the notion of cointegration when two asset prices are generated by a driftless Itô-semimartingale featuring jumps with infinite activity, observed regularly and synchronously at high frequency. We develop a regression based estimation of the cointegrated relations method …

Federated learning has a variety of applications in multiple domains by utilizing private training data stored on different devices. However, the aggregation process in federated learning is highly vulnerable to adversarial attacks so that the global model may behave abnormally under attacks. To tackle this challenge, …

Adaptive sampling detects local concept drift with limited labels.

New method for Sharpe ratio analysis in high dimensions using residual-based nodewise regression.

We present a new physics informed neural network (PINN) algorithm for solving brittle fracture problems. While most of the PINN algorithms available in the literature minimize the residual of the governing partial differential equation, the proposed approach takes a different path by minimizing the variational energy o…

DeepSVM learns SVMs without PDE solving, achieving high pricing accuracy.

We revisit residual algorithms in both model-free and model-based reinforcement learning settings. We propose the bidirectional target network technique to stabilize residual algorithms, yielding a residual version of DDPG that significantly outperforms vanilla DDPG in the DeepMind Control Suite benchmark. Moreover, we…

Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present an overview of physics-informed neural networks (PINNs), which embed a PDE into the loss of the neural network using automatic differentiat…

Financial econometrics has become an increasingly popular research field. In this paper we review a few parametric and nonparametric models and methods used in this area. After introducing several widely used continuous-time and discrete-time models, we study in detail dependence structures of discrete samples, includi…

Two methods are proposed to filter correlations in DCC-GARCH residuals for foreign exchange rates.

Flexible framework integrates machine learning and DRO for uncertain parameter prediction.

ResGCN detects anomalies in attributed networks by capturing sparsity and nonlinearity.

New inequality for refined knot invariants in a specific space.

We study refined topological string theory in the presence of orientifolds by counting second-quantized BPS states in M-theory. This leads us to propose a new integrality condition for both refined and unrefined topological strings when orientifolds are present. We define the SO(2N) refined Chern-Simons theory which co…

A new method boosts exploration in bandit algorithms, reducing regret.

Refines neural network predictions using background knowledge for improved accuracy.

New research shows label refinement and weak training have limitations for aligning LLMs.

We refine Khovanov homology in the presence of an involution on the link. This refinement takes the form of a triply-graded theory, arising from a pair of filtrations. We focus primarily on strongly invertible knots and show, for instance, that this refinement is able to detect mutation.

In a previous paper we constructed a spectrum-level refinement of Khovanov homology. This refinement induces stable cohomology operations on Khovanov homology. In this paper we show that these cohomology operations commute with cobordism maps on Khovanov homology. As a consequence we obtain a refinement of Rasmussen's …

Refined 3D index uses surgery and gradings to distinguish 3-manifolds.

With the ever-increasing reliance on data for data-driven applications in power grids, such as event cause analysis, the authenticity of data streams has become crucially important. The data can be prone to adversarial stealthy attacks aiming to manipulate the data such that residual-based bad data detectors cannot det…

Birg{é} and Massart proposed in 2001 the slope heuristics as a way to choose optimally from data an unknown multiplicative constant in front of a penalty. It is built upon the notion of minimal penalty, and it has been generalized since to some "minimal-penalty algorithms". This paper reviews the theoretical results ob…

Paper improves confidence intervals and variance estimation for deep learning models.

Refines deep generative models to improve data density precision.

Established a stable cohomotopy refinement for Pin(2) monopole invariants.

Refined 1-cocycle for knots helps quantify isotopies.

New method recovers causal order from dependent data.

Braverman and Kappeler introduced a refinement of the Ray-Singer analytic torsion associated to a flat vector bundle over a closed odd-dimensional manifold. We study this notion and improve the Braverman-Kappeler theorem comparing the refined analytic torsion with Farber-Turaev refinement of the combinatorial torsion. …

We note that our stable homotopy refinements of Khovanov's arc algebras and tangle invariants induce refinements of Chen-Khovanov and Stroppel's platform algebras and tangle invariants, and discuss the topological Hochschild homology of these refinements.

Bayesian model predicts oncology demand trends with high accuracy.

Estimates variance function using aggregation methods in regression models.

EGR refines and assesses protein complex structures.

A novel framework refines diffusion models iteratively for better downstream reward optimization.

We formulate large $N$ duality of $\mathrm{U}(N)$ refined Chern-Simons theory with a torus knot/link in $S^3$. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string theory with D4-branes on the $Ω$-background. This form enables us to relate refined C…

Study uses AI to refine loan assessments, improving credit default predictions.

Let $E$ be a flat complex vector bundle over a closed oriented odd dimensional manifold $M$ endowed with a flat connection $\nabla$. The refined analytic torsion for $(M,E)$ was defined and studied by Braverman and Kappeler. Recently Mathai and Wu defined and studied the analytic torsion for the twisted de Rham complex…

The refined analytic torsion, defined by M. Braverman and T. Kappeler on closed manifolds, can be viewed as a refinement of the Ray-Singer torsion, since it is a canonical choice of an element with Ray-Singer norm one, in case of unitary representations. The complex phase of the refinement is given by the rho-invariant…

Refined BN-S model improves crude oil hedging with machine learning.

We review the construction and context of a stable homotopy refinement of Khovanov homology.

Simple models are preferred over complex models, but over-simplistic models could lead to erroneous interpretations. The classical approach is to start with a simple model, whose shortcomings are assessed in residual-based model diagnostics. Eventually, one increases the complexity of this initial overly simple model a…

The concept of refinement from probability elicitation is considered for proper scoring rules. Taking directions from the axioms of probability, refinement is further clarified using a Hilbert space interpretation and reformulated into the underlying data distribution setting where connections to maximal marginal diver…

We construct a canonical element, called the refined analytic torsion, of the determinant line of the cohomology of a closed oriented odd-dimensional manifold M with coefficients in a flat complex vector bundle E. We compute the Ray-Singer norm of the refined analytic torsion. In particular, if there exists a flat Herm…

Refined invariants for 4D 2-handlebodies, linking quantum groups and cohomology.

This paper improves the Diversification Quotient (DQ) for better risk management.