This research develops efficient surrogate models for predicting crack growth in metal structures.
problem Accurately predicting crack growth in metal structures under uncertainty.
method Employing Gaussian Process (GP) regression models for latent variable modeling to create probabilistic surrogate models.
result Surrogate models successfully encode material and load-related uncertainties in stochastic crack growth processes.
Bayesian model predicts crack evolution on rails with uncertainties.
problem Predicting crack evolution on railways due to complex interactions and uncertainties.
method Robust Bayesian multi-horizon approach with constraints.
result Trade-off between prediction accuracy and constraint compliance.
This paper improves Gaussian process predictions by integrating prior knowledge.
problem Gaussian processes lack predictive power when prior information is ignored.
method Derive mean and covariance functions from previous data using weighted sums of basis functions.
result Integrating prior knowledge significantly increases look-ahead time and accuracy.
Study uses neural processes to predict and classify crack patterns in moving disks.
problem Predicting and classifying crack patterns in moving disks.
method Peridynamic theory, Convolutional Neural Networks (CNNs), and Neural Processes.
result Neural Processes provide accurate predictions even with missing or insufficient data.
New method recovers compressed crack images for automatic segmentation.
problem Recover crack images from compressed data for SHM systems.
method Generative model-based CS method for crack images.
result Generative model effectively captures crack features for segmentation.
Improved aircraft structure prediction using derivative-enhanced sparse Cholesky GP method.
problem Accurate real-time prediction of aircraft structure performance.
method Combining derivative data with a modified dynamic sparse Cholesky linear system solver.
result Improved prediction accuracy of aircraft structure performance.
Physics-informed neural network identifies and characterizes surface cracks in metals.
problem Identifying and characterizing surface-breaking cracks in metals using ultrasound.
method Physics-informed neural network (PINN) trained with ultrasonic surface wave data and adaptive activation functions.
result PINN accurately estimates the speed of sound and identifies crack locations in metals.
In modern building infrastructures, the chance to devise adaptive and unsupervised data-driven health monitoring systems is gaining in popularity due to the large availability of big data from low-cost sensors with communication capabilities and advanced modeling tools such as Deep Learning. The main purpose of this pa…
Improved growth strategies by incorporating stochastic factors in asset returns.
problem Drift uncertainty in asset returns makes growth optimization strategies sensitive.
method Study robust growth-optimization in high-dimensional incomplete markets under drift uncertainty and ergodicity.
result Utilizing stochastic factors improves robust growth rates and optimal strategies.
Deep-CAPTCHA cracks visual CAPTCHAs using deep learning.
problem Cracking visual CAPTCHAs to assess vulnerabilities.
method Developed a Convolutional Neural Network (Deep-CAPTCHA) to solve numerical and alphanumeric CAPTCHAs.
result Cracking accuracy of 98.94% and 98.31% for numerical and alphanumeric datasets respectively.
This paper analyzes the robust growth rate of leveraged ETFs under uncertain parameters.
problem Analyzing the robust long-term growth rate of leveraged ETFs with uncertain parameters.
method Derive worst-case parameters using comparison principle and martingale extraction method.
result Explicitly obtain robust long-term growth rates under various models.
Effects of randomness on non-integer power law tails in multiplicatively interacting stochastic processes are investigated theoretically. Generally, randomness causes decrease of the exponent of tails and the growth rate of processes. Explicit calculations are performed for two examples: uniformly distributed and two p…
This paper tackles robust growth maximization with stochastic factors, finding optimal strategies independent of the factor process.
problem Maximizing asymptotic growth under model uncertainty with stochastic factor processes.
method Combines techniques from partial differential equations, calculus of variations, and generalized Dirichlet forms.
result Optimal trading strategy is functionally generated and independent of the stochastic factor process.
In this paper, a new theory is developed for first-order stochastic convex optimization, showing that the global convergence rate is sufficiently quantified by a local growth rate of the objective function in a neighborhood of the optimal solutions. In particular, if the objective function F(w) in the ε-sub…
It has been suggested in 1999 that a certain volume growth condition for geodesically complete Riemannian manifolds might imply that the manifold is stochastically complete. This is motivated by a large class of examples and by a known analogous criterion for recurrence of Brownian motion. We show that the suggested im…
The Kelly rule fails to maximize growth in a time-changed return setting.
problem Performance of the Kelly rule in a time-changed return process.
method Investigated the Kelly rule in a semi-martingale setting with a time change process.
result The Kelly rule does not maximize average growth rate in a non-normal log-return setting.
The study extends stochastic completeness to landmark spaces with any number of landmarks.
problem Stochastic completeness for landmark spaces with arbitrary numbers of landmarks.
method Volume growth criterion and eigenvalue bounds for geodesic balls.
result Stochastic completeness for landmark spaces with any number of landmarks is proven.
Study growth of LP wealth in G3Ms affected by trading fees and arbitrage.
problem Analyzing profitability of LPs in G3Ms under trading fees and arbitrage.
method Stochastic reflected diffusion processes to model G3M dynamics.
result Long-term expected logarithmic growth of LP wealth calculated.
Given data over the joint distribution of two random variables X and Y, we consider the problem of inferring the most likely causal direction between X and Y. In particular, we consider the general case where both X and Y may be univariate or multivariate, and of the same or mixed data types. We take an inf…
Owing to the expeditious growth in the information and communication technologies, smart cities have raised the expectations in terms of efficient functioning and management. One key aspect of residents' daily comfort is assured through affording reliable traffic management and route planning. Comprehensively, the majo…
Study proves optimal controls for stochastic Volterra equations with singular kernels.
problem Existence of optimal controls for stochastic Volterra equations with singular kernels.
method Sufficient conditions based on integrability and growth hypotheses.
result Existence of optimal relaxed and strict controls under classical convexity assumptions.
Study optimizes growth rate for investors with long-only constraints.
problem Maximizing growth rate under drift uncertainty and long-only constraints.
method Developed a finite dimensional approximation for concave functionally generated portfolios.
result Proved uniqueness and existence for optimal portfolios under long-only constraints.
RELTA-SGLD stabilizes nonconvex SGLD updates with a lighter taming scheme.
problem Stabilizing superlinear stochastic-gradient updates in nonconvex optimization.
method Threshold-based taming with relative-growth principle for stability.
result Polynomial moment stability and first-order stationary accuracy in nonconvex SGLD.
Dividend discount models have been developed in a deterministic setting. Some authors (Hurley and Johnson, 1994 and 1998; Yao, 1997) have introduced randomness in terms of stochastic growth rates, delivering closed-form expressions for the expected value of stock prices. This paper extends such previous results by dete…
We consider the problem of finding optimal strategies that maximize the average growth-rate of multiplicative stochastic processes. For a geometric Brownian motion the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction o…
New algorithm tames non-linear growth in stochastic optimization.
problem Computational challenges in E-step of EM framework.
method Employing interacting particle systems and taming techniques to create tIPLA.
result Non-asymptotic convergence error estimates in Wasserstein-2 distance for tIPLA.
Study finds billing codes at IPO boost digital health companies' financial performance.
problem Identifying factors that drive long-term financial success in digital health companies.
method Analyzed 33 digital health IPOs from 2010-2021, comparing companies with and without billing codes.
result Companies with billing codes at IPO were significantly more likely to achieve positive CAGR and higher market capitalization.
We demonstrate by mathematical analysis and systematic computer simulations that redistribution can lead to sustainable growth in a society. The human capital dynamics of each agent is described by a stochastic multiplicative process which, in the long run, leads to the destruction of individual human capital and the e…
In this letter we investigate the information provided by the "compass rose" (Crack, T.F. and Ledoit, O. (1996), Journal of Finance, 51(2), pg. 751-762) patterns revealed in phase portraits of daily stock returns. It has been initially suggested that the compass rose is just a manifestation of price clustering and disc…
In this paper, five different approaches for reduced-order modeling of brittle fracture in geomaterials, specifically concrete, are presented and compared. Four of the five methods rely on machine learning (ML) algorithms to approximate important aspects of the brittle fracture problem. In addition to the ML algorithms…
New approach uses 'growth' and 'harvesting' concepts to improve deep learning models.
problem Current deep learning models lack transparency and high convergence rates.
method Reconsider neural networks as single-species population dynamics with balanced growth and harvesting rates.
result SGD with balanced growth and harvesting rates outperforms adaptive methods in all three requirements.
DAFNO learns surrogates for complex systems on irregular geometries.
problem Learning accurate surrogates for complex physical systems on irregular geometries.
method DAFNO incorporates a smoothed characteristic function in the integral layer architecture of FNOs, leveraging FFT for rapid computations.
result DAFNO achieves state-of-the-art accuracy on material modeling and airfoil simulation datasets.
HNPE uses auxiliary data to estimate parameters in uncertain models.
problem Uncertain models with identical observations.
method Exploits global parameters from auxiliary data to estimate parameters.
result Validated on a motivating example and applied to neuroscience.
In this paper we give a complete description of the set of discrete faithful representations SH(M) uniformizing a compact, orientable, hyperbolizable 3-manifold M with incompressible boundary, equipped with the strong topology, with the description given in term of the end invariants of the quotient manifolds. As part …
Model quantifies cyber-attacks' impact on firms and insurers.
problem Impact of cyber-attacks on firms' revenues and insurers' portfolios.
method Stochastic SIR model coupled with granular firm growth model.
result Predicts insurer needs to compensate up to two days of revenue in a 100-day incident.
Stable cooperation emerges in fluctuating environments.
problem Evolutionary stability of cooperation in fluctuating conditions.
method Agents with fluctuating wealth share public goods, leading to cooperation.
result Agents with cooperation produce an advantage in fluctuating environments.
We construct normed spaces of real-valued functions with controlled growth on possibly infinite-dimensional state spaces such that semigroups of positive, bounded operators (Pt)t≥0 thereon with limt→0+Ptf(x)=f(x) are in fact strongly continuous. This result applies to prove optimal rates of converge…
Study optimal healthcare spending under Epstein-Zin preferences for longevity.
problem Optimizing healthcare spending to extend longevity under Epstein-Zin preferences.
method Formulated Epstein-Zin utilities over a controllable random horizon using backward stochastic differential equations and HJB equations.
result Calibrated model accurately reflects actual mortality data and compares healthcare efficacy between countries.
Proves global well-posedness for superquadratic BSDEs without Markovian assumption.
problem Global well-posedness of multidimensional superquadratic BSDEs without Markovian assumption.
method Interplay between local well-posedness of FBSDEs and backward iterations of superquadratic BSDEs.
result Global well-posedness of superquadratic BSDEs proved.
Tax dynamics affects wealth distribution in a linearly growing socio-economic model.
problem Analyzing how tax policies impact wealth distribution in a stochastic resetting system.
method Analytical and numerical study of a system of agents with linear wealth growth, stochastic resetting, and tax redistribution.
result Optimal taxation leads to economic equality, while excessive taxation results in reverse disparity.
Neural networks can approximate complex stochastic equations well.
problem Approximating general stochastic differential equations.
method Identified neural network classes approximating continuous functions.
result Neural stochastic differential equations can approximate general stochastic differential equations arbitrarily well.
This paper studies the long-term growth rate of expected utility from holding a leveraged exchanged-traded fund (LETF), which is a constant proportion portfolio of the reference asset. Working with the power utility function, we develop an analytical approach that employs martingale extraction and involves finding the …
Game theory model shows optimal investment strategy for wealth growth.
problem Minimizing time to reach large wealth in a stochastic asset market.
method Proved strategy of proportional asset investment minimizes expected time.
result Proportional investment strategy asymptotically minimizes time to large wealth.
The aim of this work is to extend the capital growth theory developed by Kelly, Breiman, Cover and others to asset market models with transaction costs. We define a natural generalization of the notion of a numeraire portfolio proposed by Long and show how such portfolios can be used for constructing growth-optimal inv…
RONM method reduces regret in stochastic convex bandits with decreasing noise.
problem Stochastic convex bandit problem with decreasing noise.
method Regularized Online Newton Method (RONM) based on Online Newton Method (ONM).
result RONM achieves polylogarithmic regret in time horizon n.
This article proposes a new approximation scheme for quadratic-growth BSDEs in a Markovian setting by connecting a series of semi-analytic asymptotic expansions applied to short-time intervals. Although there remains a condition which needs to be checked a posteriori, one can avoid altogether time-consuming Monte Carlo…
Paper tackles robust control of SDEs with ambiguity, proving value function existence and applying to investment problems.
problem Robust control of SDEs with ambiguity parameters and non-Lipschitz coefficients.
method Existence and uniqueness of value function established through BSDEs with non-linear growth conditions.
result Existence and uniqueness of value function in proper space, verified through BSDEs.
Optimizes portfolio growth rate for a behavioral investor considering terminal relative growth rate.
problem Optimizing a behavioral investor's portfolio growth rate under relative growth criterion.
method Martingale method, concavification, and quantile optimization techniques.
result Derives closed-form optimal growth rate and finds significant impact of benchmark growth rate.