# | Title | Journal | Year | Citations |
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1 | Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images | IEEE Transactions on Pattern Analysis and Machine Intelligence | 1984 | 13,839 |
2 | Efficient Implementation of Weighted ENO Schemes | Journal of Computational Physics | 1996 | 5,195 |
3 | Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations | Journal of Computational Physics | 2019 | 4,963 |
4 | Theory of Functional Differential Equations | Applied Mathematical Sciences (Switzerland) | 1977 | 4,014 |
5 | Neural Networks and the Bias/Variance Dilemma | Neural Computation | 1992 | 2,832 |
6 | Efficient implementation of essentially non-oscillatory shock-capturing schemes, II | Journal of Computational Physics | 1989 | 2,675 |
7 | Theory of Mechanical Damping Due to Dislocations | Journal of Applied Physics | 1956 | 1,997 |
8 | Total variation diminishing Runge-Kutta schemes | Mathematics of Computation | 1998 | 1,803 |
9 | Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems | Journal of Scientific Computing | 2001 | 1,395 |
10 | Modeling uncertainty in flow simulations via generalized polynomial chaos | Journal of Computational Physics | 2003 | 1,192 |
11 | TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One-dimensional systems | Journal of Computational Physics | 1989 | 1,152 |
12 | Hierarchical Bayesian inference in the visual cortex | Journal of the Optical Society of America A: Optics and Image Science, and Vision | 2003 | 1,085 |
13 | Stochastic Approximation Methods for Constrained and Unconstrained Systems | Applied Mathematical Sciences (Switzerland) | 1978 | 1,008 |
14 | An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws | Journal of Computational Physics | 2008 | 953 |
15 | Stability theory of solitary waves in the presence of symmetry, I | Journal of Functional Analysis | 1987 | 897 |
16 | The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields | Journal of Fluid Mechanics | 1987 | 893 |
17 | Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations | Science | 2020 | 846 |
18 | Multiple Scattering of Waves | Journal of Mathematical Physics | 1961 | 808 |
19 | On pole assignment in multi-input controllable linear systems | IEEE Transactions on Automatic Control | 1967 | 772 |
20 | Hidden physics models: Machine learning of nonlinear partial differential equations | Journal of Computational Physics | 2018 | 739 |
21 | Kinetics of biopolymerization on nucleic acid templates | Biopolymers | 1968 | 730 |
22 | Application of Dislocation Theory to Internal Friction Phenomena at High Frequencies | Journal of Applied Physics | 1956 | 715 |
23 | Stochastic Approximation Algorithms and Applications | Journal of Applied Physics | 1997 | 714 |
24 | Distinguished material surfaces and coherent structures in three-dimensional fluid flows | Physica D: Nonlinear Phenomena | 2001 | 691 |
25 | Decoupling in the design and synthesis of multivariable control systems | IEEE Transactions on Automatic Control | 1967 | 690 |
26 | Convergence of approximation schemes for fully nonlinear second order equations | Asymptotic Analysis | 1991 | 687 |
27 | The Contact Problem for Viscoelastic Bodies | Journal of Applied Mechanics, Transactions ASME | 1960 | 604 |
28 | Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators | Nature Machine Intelligence | 2021 | 589 |
29 | Scattering of a Plane Longitudinal Wave by a Spherical Obstacle in an Isotropically Elastic Solid | Journal of Applied Physics | 1956 | 566 |
30 | The Non-Linear Field Theories of Mechanics | Journal of Applied Physics | 1992 | 486 |
31 | Option Pricing Under a Double Exponential Jump Diffusion Model | Management Science | 2004 | 476 |
32 | An adaptive multi-element generalized polynomial chaos method for stochastic differential equations | Journal of Computational Physics | 2005 | 474 |
33 | Physics-informed neural networks for high-speed flows | Computer Methods in Applied Mechanics and Engineering | 2020 | 464 |
34 | Ordinary and Delay Differential Equations | Applied Mathematical Sciences (Switzerland) | 1977 | 463 |
35 | A Multiscale Red Blood Cell Model with Accurate Mechanics, Rheology, and Dynamics | Biophysical Journal | 2010 | 460 |
36 | Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos | Computer Methods in Applied Mechanics and Engineering | 2002 | 455 |
37 | Runge–Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes | Journal of Computational Physics | 2008 | 426 |
38 | On maximum-principle-satisfying high order schemes for scalar conservation laws | Journal of Computational Physics | 2010 | 417 |
39 | Numerical Methods for Stochastic Control Problems in Continuous Time | Journal of Computational Physics | 1992 | 416 |
40 | On Advances in Statistical Modeling of Natural Images | Journal of Mathematical Imaging and Vision | 2003 | 388 |
41 | NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations | Journal of Computational Physics | 2021 | 386 |
42 | The Development of Discontinuous Galerkin Methods | Lecture Notes in Computational Science and Engineering | 2000 | 381 |
43 | Bayesian Population Decoding of Motor Cortical Activity Using a Kalman Filter | Neural Computation | 2006 | 380 |
44 | A Stable and Conservative Interface Treatment of Arbitrary Spatial Accuracy | Journal of Computational Physics | 1999 | 375 |
45 | Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations | ESAIM: Mathematical Modelling and Numerical Analysis | 2007 | 373 |
46 | Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems | Computer Methods in Applied Mechanics and Engineering | 2020 | 362 |
47 | Convergence of Proportional-Fair Sharing Algorithms Under General Conditions | IEEE Transactions on Wireless Communications | 2004 | 357 |
48 | B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data | Journal of Computational Physics | 2021 | 350 |
49 | On head-on collisions between two solitary waves | Journal of Fluid Mechanics | 1980 | 336 |
50 | Dynamics and low-dimensionality of a turbulent near wake | Journal of Fluid Mechanics | 2000 | 331 |