Article
Computer Science, Artificial Intelligence
Jure Brence, Ljupco Todorovski, Sago Dzeroski
Summary: This paper proposes the use of probabilistic context-free grammars in equation discovery, encoding soft constraints to specify a prior probability distribution on the space of possible equations. It demonstrates that this approach is more efficient than using deterministic grammars in the context of equation discovery, and lays the foundations for Bayesian approaches to equation discovery by specifying prior probability distributions over equation spaces.
KNOWLEDGE-BASED SYSTEMS
(2021)
Article
Computer Science, Information Systems
Jure Brence, Saso Dzeroski, Ljupco Todorovski
Summary: This paper proposes using attribute grammars to ensure the dimensional consistency of the induced equations, which can combine cross-domain knowledge and domain-specific knowledge effectively. The study also demonstrates that attribute grammars can be transformed into probabilistic context-free grammars for equation discovery efficiently. Furthermore, empirical evidence shows that attribute grammars ensuring dimensional consistency of equations can significantly improve the performance of equation discovery on the standard set of a hundred Feynman benchmarks.
INFORMATION SCIENCES
(2023)
Article
Engineering, Multidisciplinary
Yasen Wang, Huazhen Fang, Junyang Jin, Guijun Ma, Xin He, Xing Dai, Zuogong Yue, Cheng Cheng, Hai-Tao Zhang, Donglin Pu, Dongrui Wu, Ye Yuan, Jorge Goncalves, Juergen Kurths, Han Ding
Summary: This study presents a novel framework for identifying stochastic differential equations (SDEs) by leveraging sparse Bayesian learning (SBL) technique. The framework automatically searches for a parsimonious representation from the space of candidate basis functions using SBL and formulates the linear regression problem for the discovery of SDEs in an efficient way. The effectiveness of the proposed framework is demonstrated using real and simulated data.
Article
Mathematics, Applied
Vicente J. Bevia, Juan C. Cortes, Marc Jornet, Rafael J. Villanueva
Summary: In this study, a pathwise solution to a general scalar random differential equation with state-dependent Dirac-delta impulse terms at specific time instants is rigorously constructed. Additionally, the first probability density function of the solution is obtained by combining the Liouville-Gibbs equation and the Random Variable Transformation technique. The theoretical findings are further illustrated through computational simulations on two widely-used stochastic models in mathematical modeling.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Computer Science, Artificial Intelligence
Pengfei Zhang, Xiang Cheng, Sen Su, Ning Wang
Summary: This paper proposes a solution called TESLA, which aims to obtain accurate truths under rigorous local differential privacy. It introduces a runtime filtering mechanism, a probabilistic fusion mechanism, and a probabilistic weight mechanism to mitigate the negative effects of injected noise and inherent Gaussian noise.
KNOWLEDGE-BASED SYSTEMS
(2023)
Article
Mathematics, Interdisciplinary Applications
T. Oraby, E. Suazo, H. Arrubla
Summary: The work in this paper has four aspects. Firstly, an alternative approach is introduced to solve fractional ordinary differential equations by representing them as the expected value of a random time process. Secondly, based on Monte Carlo integration, an interesting numerical method is presented to simulate solutions of fractional ordinary and partial differential equations. Thirdly, it is shown that this approach can find the fundamental solutions for fractional partial differential equations, where the fractional derivative in time is in the Caputo sense and the fractional derivative in space is in the Riesz-Feller sense. Lastly, using the Riccati equation, families of fractional partial differential equations with variable coefficients that have explicit solutions are studied, and these solutions connect Lie symmetries to fractional partial differential equations.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics
Antonios Charalambopoulos, Leonidas Gergidis, Eleftheria Vassilopoulou
Summary: In this study, a novel stochastic method is developed to address the time-reduced inverse scattering problem governed by the Helmholtz equation. Stochastic representations of the scattering field are constructed based on stochastic analysis, providing an alternative approach to solve the direct and inverse scattering problem locally. Two different schemes are proposed for the reconstruction from far field and near field data, respectively.
Article
Mathematics, Interdisciplinary Applications
Xiaohu Yu, Airong Chen, Haocheng Chang
Summary: This paper presents a novel nonlocal numerical paradigm using the peridynamic differential operator for solving a class of general nonlinear ordinary differential equations. The local differential form of differential governing equations and initial/boundary conditions are reformulated into the nonlocal integral form using a meshless orthogonal technique. The proposed method utilizes the Lagrange multiplier method and the variational principle, and is applied to solve nonlinear ordinary differential equations with initial/boundary conditions through the Newton-Raphson iteration method. Benchmark problems and the galloping vibration problem are solved to demonstrate the applicability and accuracy of the proposed numerical method, and the results are consistent with previous literature.
COMPUTATIONAL PARTICLE MECHANICS
(2023)
Article
Engineering, Multidisciplinary
C. Soize, R. Ghanem
Summary: This paper introduces a novel probabilistic learning algorithm that can solve a wide range of nonlinear stochastic boundary value problems depending on vector-valued random control parameters. The algorithm allows for generating a large number of learned realizations of stochastic processes and their corresponding random control parameters, and generates these realizations by minimizing the vector-valued random residual of the PDE.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mathematics
Carmen Ionescu, Radu Constantinescu
Summary: The paper presents a method for reducing the differentiability order of an ordinary differential equation by defining the first derivative as a function. It introduces the concept of an attached flow equation and proposes a specific balancing procedure for choosing the flow. The effectiveness of the method is demonstrated by solving important equations in soliton theory.
Article
Nuclear Science & Technology
Tamas Zoltan Hajas, Gabor Tolnai, Mark Margoczi, David Legrady
Summary: The Dynamic Monte Carlo (DMC) method is a relevant tool for kinetic calculations and simulations of coupled neutronics-thermal-hydraulics problems. It provides high fidelity calculations in detailed and complex geometries, but requires high computational resources. The stochastic nature of DMC results poses challenges in terms of stability and convergence in coupled DMC and thermal-hydraulics simulations. This paper introduces a Stochastic Differential Equations (SDEs) approach to connect the DMC method with differential equation formalism and presents a Non-Analog Monte Carlo (NAMC) model for the Stochastic Point-Kinetics equation (SPKe). Analytic solutions for random variates, reactor power expectation, and variance are given. A comparison is made between the analytic variance obtained from Monte Carlo simulations and the calculations from GUARDYAN code in different reactor models.
ANNALS OF NUCLEAR ENERGY
(2024)
Article
Engineering, Mechanical
Zhiming Zhang, Yongming Liu
Summary: This study proposes a model selection criterion for discovering the governing Partial Differential Equations (PDEs) of nonlinear dynamical systems. A new PESBL method is developed to enhance the simplicity and sparsity of the learned model. The proposed method evaluates the parsimony of model terms based on their locations in the candidate library and updates model parameters through Bayesian inference.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2022)
Article
Computer Science, Artificial Intelligence
Robert Stephany, Christopher Earls
Summary: A new approach using two neural networks and sparse regression algorithm is introduced for discovering predictive models of complex physical systems, showing robustness in dealing with noisy and limited measurements.
Proceedings Paper
Computer Science, Artificial Intelligence
Bostjan Gec, Nina Omejc, Jure Brence, Saso Dzeroski, Ljupco Todorovski
Summary: The paper presents a novel method for inferring ODEs from data, which extends an existing equation discovery method. It can infer ODEs from partial observations of dynamical systems and has shown improved reconstruction performance compared to state-of-the-art methods.
DISCOVERY SCIENCE (DS 2022)
(2022)
Article
Mathematics, Applied
Juan-C Cortes, Sandra E. Delgadillo-Aleman, Roberto A. Ku-Carrillo, Rafael-J Villanueva
Summary: This study examines a class of non-homogeneous first-order linear random differential equations subject to an infinite sequence of random intensity square impulses. These equations are useful in modeling the dynamics of a population with periodic harvesting and migration under uncertainties. The solution is explicitly obtained via the first probability density function, and probabilistic stability analysis is conducted through the densities of random sequences of minima and maxima.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Ecology
Patricia A. Soranno, Kendra Spence Cheruvelil, Boyang Liu, Qi Wang, Pang-Ning Tan, Jiayu Zhou, Katelyn B. S. King, Ian M. McCullough, Jemma Stachelek, Meridith Bartley, Christopher T. Filstrup, Ephraim M. Hanks, Jean-Francois Lapierre, Noah R. Lottig, Erin M. Schliep, Tyler Wagner, Katherine E. Webster
ECOLOGICAL APPLICATIONS
(2020)
Article
Environmental Sciences
Joshua S. North, Erin M. Schliep, Christopher K. Wikle
Summary: Statistical methods are necessary to quantify uncertainty in environmental processes like seasonal temperature cycles, where both annual and semi-annual harmonics play important roles. A proposed multivariate spatiotemporal model captures the spatial and temporal changes in temperature seasonal cycles due to different harmonics, providing insights into regions experiencing significant changes in temperature patterns.
Article
Social Sciences, Mathematical Methods
Erin M. Schliep, Alan E. Gelfand, Jesus Abaurrea, Jesus Asin, Maria A. Beamonte, Ana C. Cebrian
Summary: Research indicates that global warming leads to more warm days and frequent heat waves. A spatio-temporal model is proposed to study extreme heat events, using local thresholds to predict the characteristics of EHEs at unobserved locations. The model outperforms an autoregressive model based on out-of-sample prediction.
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES A-STATISTICS IN SOCIETY
(2021)
Article
Ecology
Sydney N. Bailey, Grant P. Elliott, Erin M. Schliep
Summary: Based on the study of seedling establishment at upper treeline in the Southern Rocky Mountains, it was found that temperature-moisture interactions are crucial for successful seedling establishment, and there has been a complete lack of establishment in the entire region over the past decade. This could indicate that climatic conditions above treeline have surpassed the optimum for successful seedling establishment.
Article
Engineering, Environmental
Ana C. Cebrian, Jesus Asin, Alan E. Gelfand, Erin M. Schliep, Jorge Castillo-Mateo, Maria A. Beamonte, Jesus Abaurrea
Summary: This study aims to formalize the spatial extent of extreme heat events using time series and spatial information, conducting risk assessment in the Comunidad Autonoma de Aragon in northeastern Spain. The research finds that the extent of extreme heat events may increase over time as evidenced by comparisons across decades.
STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT
(2022)
Article
Green & Sustainable Science & Technology
Ashkan Mirzaee, Ronald G. McGarvey, Francisco X. Aguilar, Erin M. Schliep
Summary: Biopower, as a significant source of renewable energy in the US, shows positive ecological conditions and carbon balances. The study found that timberland areas around biopower plants have more live and standing-dead trees, and carbon stocks compared to areas around coal-burning plants. With longer biopower generation, there is an upward trend in carbon stocks within live trees.
ENVIRONMENT DEVELOPMENT AND SUSTAINABILITY
(2023)
Article
Biology
Joshua S. North, Christopher K. Wikle, Erin M. Schliep
Summary: This paper presents a Bayesian data-driven approach to nonlinear dynamic equation discovery, which can learn the governing equations of complex systems and improve our understanding of the mechanisms.
JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS
(2022)
Article
Multidisciplinary Sciences
Tyler Wagner, Erin M. Schliep, Joshua S. North, Holly Kundel, Christopher A. Custer, Jenna K. Ruzich, Gretchen J. A. Hansen
Summary: By combining observations of species abundance and environmental conditions with laboratory-derived data on the physiological response of poikilotherms to temperature, a physiologically guided abundance (PGA) model was developed to predict species geographical distributions and abundance in response to climate change. The model incorporates uncertainty in laboratory-derived thermal response curves and provides estimates of thermal habitat suitability and extinction probability based on site-specific conditions. The results show that considering physiological information greatly affects temperature-driven changes in distributions, local extinction, and abundance of cold, cool, and warm-adapted species. Failure to account for species-specific physiological constraints could lead to unrealistic predictions under a warming climate.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2023)
Article
Biodiversity Conservation
Joshua S. North, Erin M. Schliep, Gretchen J. A. Hansen, Holly Kundel, Christopher A. Custer, Paul Mclaughlin, Tyler Wagner
Summary: Estimating relative abundance is crucial for conservation and management efforts in freshwater fisheries. This study developed a joint species distribution model (JSDM) that accounts for varying sampling conditions and captures seasonal variation in species life history. The findings show that not accounting for these variations can bias the inference of relative abundance, limiting our ability to detect responses to management interventions and environmental change. The model can be applied to other systems where catchability may vary as a function of space, time, and species.
JOURNAL OF APPLIED ECOLOGY
(2023)
Article
Social Sciences, Mathematical Methods
Erin M. Schliep, Toryn L. J. Schafer, Matthew Hawkey
Summary: Subjective wellness data is crucial for understanding the well-being of athletes and optimizing their performance, especially in terms of training and recovery effects. A multivariate latent factor model was developed to study the impact of training and recovery on athlete wellness. The study found that individual responses to training and recovery can vary, highlighting the importance of using a multivariate approach to monitor athlete wellness.
JOURNAL OF QUANTITATIVE ANALYSIS IN SPORTS
(2021)
