Article
Engineering, Electrical & Electronic
Zhizhen Zhao, Jong Chul Ye, Yoram Bresler
Summary: Physics-informed generative modeling is a rapidly growing field in computational imaging, with various methods and applications. This review focuses on generative modeling techniques, such as variational autoencoders (VAEs) and generative adversarial networks (GANs), and recent advancements in score-based generative models. Through different imaging applications, the review demonstrates how these generative modeling techniques effectively incorporate the physics of the imaging problem to solve inverse problems.
IEEE SIGNAL PROCESSING MAGAZINE
(2023)
Article
Computer Science, Artificial Intelligence
Markus Pantsar
Summary: In computational complexity theory, decision problems are categorized into complexity classes, with functions in P considered tractable and first-order logic systems linked to P. Second-order logic systems are deemed computationally intractable and may not be suitable for modeling human cognitive abilities.
MINDS AND MACHINES
(2021)
Article
Mechanics
Philipp Reiter, Xuan Zhang, Olga Shishkina
Summary: This work investigates the effects of different thermal sidewall boundary conditions on flow states and heat transport in Rayleigh-Benard convection. The study finds that different thermal conditions at the sidewall lead to significant differences in heat transport, but these differences become less pronounced for larger Rayleigh numbers.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Chemistry, Physical
Sharon Hammes-Schiffer
Summary: The NEO approach incorporates nuclear quantum effects and non-Born-Oppenheimer behavior into quantum chemistry calculations and molecular dynamics simulations, dealing with nuclear delocalization, zero-point energy, excited state processes, etc. It offers conceptual simplicity and computational efficiency, showing promising prospects for future developments in diverse chemical and biological systems.
JOURNAL OF CHEMICAL PHYSICS
(2021)
Review
Multidisciplinary Sciences
Valerio Capraro, Matjaz Perc
Summary: One-shot anonymous unselfishness in economic games is commonly explained by social preferences, but recent research shows that it is better explained by preferences for following one's own personal norms. This moral preference hypothesis can be used to increase charitable donations by making the morality of an action salient.
JOURNAL OF THE ROYAL SOCIETY INTERFACE
(2021)
Article
Computer Science, Artificial Intelligence
Yunqi Li, Hanxiong Chen, Shuyuan Xu, Yingqiang Ge, Juntao Tan, Shuchang Liu, Yongfeng Zhang
Summary: This survey provides a systematic overview of existing works on fairness in recommendation, introducing fundamental concepts of fairness and presenting methods and challenges in considering fairness in recommender systems.
ACM TRANSACTIONS ON INTELLIGENT SYSTEMS AND TECHNOLOGY
(2023)
Review
Physiology
Jussi T. Koivumaki, Johan Hoffman, Mary M. Maleckar, Gaute T. Einevoll, Joakim Sundnes
Summary: Mathematical models have greatly advanced cardiovascular physiology research, but barriers between experimental and computational approaches remain, calling for closer integration.
Article
Mechanics
Shengze Cai, Zhicheng Wang, Frederik Fuest, Young Jin Jeon, Callum Gray, George Em Karniadakis
Summary: This research proposes a new method based on physics-informed neural networks to infer full continuous three-dimensional velocity and pressure fields from Tomo-BOS imaging. Validation on synthetic and real data demonstrates the accuracy and feasibility of the method.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Engineering, Multidisciplinary
Mauro Passarotto, Silvano Pitassi, Ruben Specogna
Summary: This paper presents an improved integral method for solving eddy current problems. By introducing new basis functions and inductance matrix compression techniques, it effectively addresses the issues of slow computation speed and large memory occupation in volume integral methods.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
Vivek S. Yadav, Naveen Ganta, Bikash Mahato, Manoj K. Rajpoot, Yogesh G. Bhumkar
Summary: This paper presents a new class of implicit Runge-Kutta time-marching methods (CERK) for solving the compressible Navier-Stokes equations in two and three dimensions. The developed CERK methods do not require any numerical or analytical inversion of the coefficient matrix, making them efficient and robust. The performance of the methods is validated by solving the convection-diffusion equation and the unsteady compressible Navier-Stokes equations, and compared with other explicit and implicit methods in the literature. The methods are also applied to benchmark problems in computational aeroacoustics, producing results that match well with numerical and experimental data.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Chemistry, Multidisciplinary
Bexy Alfonso, Joaquin Taverner, Emilio Vivancos, Vicente Botti
Summary: This work explores the possibility of building generic computational approaches and languages to model affective phenomena. By conducting an analysis inspired by philosophical and psychological theories, a theoretical framework is proposed to support the development of a model of an affective agent with practical reasoning. The framework also allows for incremental research and evaluation of current computational approaches in integrating practical reasoning and affect-related issues.
APPLIED SCIENCES-BASEL
(2021)
Article
Computer Science, Artificial Intelligence
Huu Le, Tat-Jun Chin, Anders Eriksson, Thanh-Toan Do, David Suter
Summary: Maximum consensus estimation is crucial in robust fitting problems in computer vision. Existing algorithms either provide rough approximate solutions cheaply or exact solutions at a high cost. This paper proposes deterministic algorithms to approximately optimize the maximum consensus criterion, filling the gap between the two extremes. The algorithms, based on convex subproblem solving, greatly improve rough initial estimates and are practical for realistic input sizes.
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
(2021)
Article
Computer Science, Hardware & Architecture
Andre Souza, Nelson Costa, Joao Pedro, Joao Pires
Summary: Due to the high potential of multi-band transmission (MBT) systems as a short- to medium-term solution to the ever-increasing demand for fiber capacity, accurate models for estimating the quality of transmission (QoT) in these systems are being developed. This study analyzes the computational time and accuracy of several QoT estimation methods for MBT systems, and proposes an enhanced FWM model to consider the SRS effect. The closed-form ISRS-GN model has the best balance between computational complexity and accuracy for launch powers up to 4 dBm.
JOURNAL OF OPTICAL COMMUNICATIONS AND NETWORKING
(2023)
Article
Mathematics, Applied
Victoria B. Bekezhanova, Olga N. Goncharova
Summary: This study focuses on the exact solution of the thermoconcentration convection equations with group origin under the Oberbeck-Boussinesq approximation. The applicability of this solution in describing steady-state convective flows of liquid and co-current gas flux under conditions of inhomogeneous evaporation is discussed. Analytical algorithms are proposed to obtain the required functions for different types of boundary conditions. The influence of external thermal load and boundary thermal conditions on velocity and temperature fields, evaporation mass flow rate, and vapor content in the gas layer are investigated using the example of the HFE-7100-nitrogen system. The solution accurately predicts the characteristics of convective regimes in the two-phase system and is compared with the case of uniform evaporation.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Computer Science, Artificial Intelligence
Brais Cancela, Amparo Alonso-Betanzos
Summary: This paper introduces a unified propagation method for handling both the classic Eikonal equation and the more general static Hamilton-Jacobi equations. The method maintains low complexity while increasing accuracy by creating 'mini wave-fronts' to minimize discretization error. Experimental results demonstrate superior precision and computational efficiency compared to state-of-the-art techniques.
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
(2021)
Article
Mathematics, Applied
Michael Donello, Mark H. Carpenter, Hessam Babaee
Summary: We propose a model-driven low-rank approximation method for computing sensitivities in evolutionary systems. This approach allows for accurate and tractable computation of sensitivities with respect to a large number of parameters by extracting correlations between different sensitivities.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Physiology
Lia Gander, Simone Pezzuto, Ali Gharaviri, Rolf Krause, Paris Perdikaris, Francisco Sahli Costabal
Summary: In this study, a multi-fidelity Gaussian process classification method is proposed to efficiently determine inducible regions of arrhythmias in the atria by evaluating the atrial surface. By combining low and high resolution models, this method can predict the ablation sites of atrial fibrillation more accurately.
FRONTIERS IN PHYSIOLOGY
(2022)
Article
Computer Science, Interdisciplinary Applications
Carlos Ruiz Herrera, Thomas Grandits, Gernot Plank, Paris Perdikaris, Francisco Sahli Costabal, Simone Pezzuto
Summary: FiberNet is a method to estimate the cardiac fiber architecture of the human atria, which learns the fiber arrangement by solving an inverse problem. It can accurately capture the morphology of fibers.
ENGINEERING WITH COMPUTERS
(2022)
Article
Mathematics, Applied
Sifan Wang, Hanwen Wang, Paris Perdikaris
Summary: This paper analyzes the training dynamics of deep operator networks (DeepONets) and reveals a bias favoring approximation of functions with larger magnitudes. To correct this bias, an adaptive re-weighting method is proposed, which effectively balances the magnitude of back-propagated gradients during training. A novel network architecture that is more resilient to vanishing gradient problems is also proposed. These developments provide new insights into the training of DeepONets and significantly improve their predictive accuracy, particularly in the challenging setting of learning PDE solution operators.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Multidisciplinary Sciences
Mohamed Aziz Bhouri, Paris Perdikaris
Summary: We present a machine learning framework (GP-NODE) for Bayesian model discovery from partial, noisy and irregular observations of nonlinear dynamical systems. The proposed method utilizes differentiable programming to propagate gradient information and performs Bayesian inference with Hamiltonian Monte Carlo sampling and Gaussian Process priors, allowing for the exploitation of temporal correlations in observed data and efficient inference of posterior distributions over plausible models.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Article
Engineering, Multidisciplinary
Yibo Yang, Georgios Kissas, Paris Perdikaris
Summary: This study presents a simple and effective method for quantifying posterior uncertainty in deep operator networks (DeepONets). The approach utilizes a frequentist approach with randomized prior ensembles and introduces an efficient vectorized implementation for fast parallel inference. The proposed method exhibits four main advantages: more robust and accurate predictions compared to deterministic DeepONets, reliable uncertainty estimates for sparse data sets with multi-scale function pairs, effective detection of out-of-distribution and adversarial examples, and seamless quantification of uncertainty due to model bias and data noise. Additionally, the study provides an optimized JAX library called UQDeepONet that can handle large model architectures, ensemble sizes, and data sets with excellent parallel performance on accelerated hardware, enabling uncertainty quantification for DeepONets in realistic large-scale applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
Mohammad Sarabian, Hessam Babaee, Kaveh Laksari
Summary: This study proposes a physics-informed deep learning framework that utilizes a reduced-order model simulation to generate high-resolution brain hemodynamic parameters, augmenting sparse clinical measurements. The framework is validated against in vivo velocity measurements obtained from MRI scans and shows potential in diagnosing cerebral vasospasm.
IEEE TRANSACTIONS ON MEDICAL IMAGING
(2022)
Article
Biophysics
Georgios Kissas, Eileen Hwuang, Elizabeth W. Thompson, Nadav Schwartz, John A. Detre, Walter R. Witschey, Paris Perdikaris
Summary: This study develops a computational framework that combines Bayesian inference with a reduced-order fluid dynamics model to predict and monitor high-risk pregnancies using noninvasive imaging techniques. The framework can infer parameters related to the development of hypertension from MRI measurements and predict hemodynamic quantities of interest.
JOURNAL OF BIOMECHANICAL ENGINEERING-TRANSACTIONS OF THE ASME
(2022)
Article
Computer Science, Interdisciplinary Applications
Shaghayegh Zamani Ashtiani, Mujeeb R. Malik, Hessam Babaee
Summary: In this work, an in situ compression technique is presented to significantly reduce the size of data storage generated by large-scale simulations of time-dependent problems. The technique is based on time-dependent subspaces and uses an adaptive strategy to control the compression error.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Engineering, Multidisciplinary
Mohammad Hossein Naderi, Hessam Babaee
Summary: Stochastic reduced-order modeling based on time-dependent bases has been successful in capturing low-dimensional manifold from stochastic partial differential equations (SPDEs). A new adaptive sparse interpolation algorithm is proposed to enable stochastic ROMs to achieve computational efficiency for nonlinear SPDEs. The algorithm constructs a low-rank approximation for the SPDE using the DEIM method, and it does not require any offline computation, allowing it to adapt to transient changes on-the-fly. The algorithm achieves computational speedup by adaptive sampling of the state and random spaces, resulting in significant reduction in computational cost for various test cases.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
Sifan Wang, Paris Perdikaris
Summary: Ordinary and partial differential equations (ODEs/PDEs) are crucial in analyzing and simulating complex dynamic processes in various fields of science and engineering. Current machine learning approaches have limitations in accurately predicting long-term behaviors of these equations. This study introduces an effective learning framework for evolution operators that can map random initial conditions to associated ODE/PDE solutions within a short time interval. The framework utilizes deep neural networks and does not require paired input-output observations. The proposed approach of temporal domain decomposition provides accurate long-term simulations for a wide range of parametric ODE and PDE systems, revolutionizing the emulation of non-equilibrium processes in science and engineering.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Engineering, Mechanical
Chengyang Mo, Paris Perdikaris, Jordan. R. R. Raney
Summary: In this work, a multifidelity Bayesian optimization framework is proposed for designing architected materials with optimal energy absorption during compression. The framework uses data from both physical experiments (high fidelity) and numerical simulations (low fidelity) to train a surrogate model, which guides the selection of the next experiments and simulations. The results show that the multifidelity approach reduces the number of iterations required to find the optimum and saves material costs and time in the optimization process. Constraints on relative density and stress variations are also incorporated into the optimization process to find optimal structures within the bounds of the constraints. This framework can be applied to other problems that involve complex, high-fidelity, labor-intensive experiments, while automating low-fidelity simulations.
JOURNAL OF ENGINEERING MECHANICS
(2023)
Article
Multidisciplinary Sciences
M. Donello, G. Palkar, M. H. Naderi, D. C. Del Rey Fernandez, H. Babaee
Summary: Time-dependent basis reduced-order models (TDB ROMs) have been successfully used to approximate the solution to nonlinear stochastic partial differential equations (PDEs). However, these models still face challenges such as inefficiency for general nonlinearities and error accumulation due to fixed rank. In this paper, a scalable method is proposed to solve TDB ROMs, which is computationally efficient, minimally intrusive, robust in the presence of small singular values, rank-adaptive, and highly parallelizable. The method utilizes oblique projections and discrete empirical interpolation method (DEIM) to evaluate the matrix differential equation at a small number of rows and columns, resulting in near-optimal matrix low-rank approximations.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2023)
Article
Energy & Fuels
Yinmin Liu, Hessam Babaee, Peyman Givi, Harsha K. Chelliah, Daniel Livescu, Arash G. Nouri
Summary: This study employs a local-sensitivity-analysis technique to generate new skeletal reaction models for methane combustion. Through calculating and analyzing the sensitivities, different levels of accuracy in reproducing the foundational fuel chemistry model (FFCM-1) results are suggested.
Proceedings Paper
Automation & Control Systems
Thomas Beckers, Jacob Seidman, Paris Perdikaris, George J. Pappas
Summary: Data-driven approaches often overlook basic physical principles in modeling complex dynamics. This study introduces a physics-informed Bayesian learning method based on Gaussian Process Port-Hamiltonian systems to address the issues of data efficiency and physical correctness.
2022 IEEE 61ST CONFERENCE ON DECISION AND CONTROL (CDC)
(2022)