{"total":116,"rows":[{"id":"2209.15616","title":"Towards Multi-spatiotemporal-scale Generalized PDE Modeling","created":"2022-09-30","cited_by_count":197,"area":null},{"id":"2110.02085","title":"Enhancing Computational Fluid Dynamics with Machine Learning","created":"2021-10-05","cited_by_count":138,"area":null},{"id":"2106.06610","title":"Scalars are universal: Equivariant machine learning, structured like classical physics","created":"2021-06-11","cited_by_count":127,"area":null},{"id":"2201.11969","title":"Approximately Equivariant Networks for Imperfectly Symmetric Dynamics","created":"2022-01-28","cited_by_count":97,"area":null},{"id":"2209.04934","title":"Clifford Neural Layers for PDE Modeling","created":"2022-09-08","cited_by_count":92,"area":null},{"id":"2109.07103","title":"Automatic Symmetry Discovery with Lie Algebra Convolutional Network","created":"2021-09-15","cited_by_count":83,"area":null},{"id":"2202.07643","title":"Lie Point Symmetry Data Augmentation for Neural PDE Solvers","created":"2022-02-15","cited_by_count":77,"area":null},{"id":"2303.10462","title":"Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review","created":"2023-03-18","cited_by_count":75,"area":null},{"id":"2207.10758","title":"DEVIANT: Depth EquiVarIAnt NeTwork for Monocular 3D Object Detection","created":"2022-07-21","cited_by_count":48,"area":null},{"id":"2306.05697","title":"Group Equivariant Fourier Neural Operators for Partial Differential Equations","created":"2023-06-09","cited_by_count":45,"area":null},{"id":"2107.01272","title":"Physics-Guided Deep Learning for Dynamical Systems: A Survey","created":"2021-07-02","cited_by_count":44,"area":null},{"id":"2302.00236","title":"Generative Adversarial Symmetry Discovery","created":"2023-02-01","cited_by_count":42,"area":null},{"id":"2102.10271","title":"Meta-Learning Dynamics Forecasting Using Task Inference","created":"2021-02-20","cited_by_count":38,"area":null},{"id":"2106.12782","title":"Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control","created":"2021-06-24","cited_by_count":38,"area":null},{"id":"2205.11912","title":"Physics-Embedded Neural Networks: Graph Neural PDE Solvers with Mixed Boundary Conditions","created":"2022-05-24","cited_by_count":33,"area":null},{"id":"2211.09231","title":"The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetry","created":"2022-11-16","cited_by_count":33,"area":null},{"id":"2210.06036","title":"Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamics","created":"2022-10-12","cited_by_count":30,"area":null},{"id":"2307.05432","title":"Self-Supervised Learning with Lie Symmetries for Partial Differential Equations","created":"2023-07-11","cited_by_count":29,"area":null},{"id":"2310.00105","title":"Latent Space Symmetry Discovery","created":"2023-09-29","cited_by_count":29,"area":null},{"id":"2303.14269","title":"The Exact Sample Complexity Gain from Invariances for Kernel Regression","created":"2023-03-24","cited_by_count":28,"area":null},{"id":"2403.04359","title":"Symmetry Considerations for Learning Task Symmetric Robot Policies","created":"2024-03-07","cited_by_count":28,"area":null},{"id":"2408.12171","title":"Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey","created":"2024-08-22","cited_by_count":28,"area":null},{"id":"2409.15771","title":"Zero-shot forecasting of chaotic systems","created":"2024-09-24","cited_by_count":28,"area":null},{"id":"2402.14730","title":"Clifford-Steerable Convolutional Neural Networks","created":"2024-02-22","cited_by_count":25,"area":null},{"id":"2410.02698","title":"Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groups","created":"2024-10-03","cited_by_count":24,"area":null},{"id":"2310.06131","title":"Learning Layer-wise Equivariances Automatically using Gradients","created":"2023-10-09","cited_by_count":23,"area":null},{"id":"2303.17078","title":"Machine Learning for Partial Differential Equations","created":"2023-03-30","cited_by_count":21,"area":null},{"id":"2110.01894","title":"Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models","created":"2021-10-05","cited_by_count":20,"area":null},{"id":"2310.02299","title":"Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolution","created":"2023-10-03","cited_by_count":20,"area":null},{"id":"2303.04745","title":"A General Theory of Correct, Incorrect, and Extrinsic Equivariance","created":"2023-03-08","cited_by_count":19,"area":null},{"id":"2406.07598","title":"Equivariance via Minimal Frame Averaging for More Symmetries and Efficiency","created":"2024-06-11","cited_by_count":19,"area":null},{"id":"2204.00887","title":"Dimensionless machine learning: Imposing exact units equivariance","created":"2022-04-02","cited_by_count":17,"area":null},{"id":"2206.09450","title":"Data Augmentation vs. Equivariant Networks: A Theory of Generalization on Dynamics Forecasting","created":"2022-06-19","cited_by_count":17,"area":null},{"id":"2206.11925","title":"Set Norm and Equivariant Skip Connections: Putting the Deep in Deep Sets","created":"2022-06-23","cited_by_count":17,"area":null},{"id":"2405.16183","title":"Graph Neural PDE Solvers with Conservation and Similarity-Equivariance","created":"2024-05-25","cited_by_count":17,"area":null},{"id":"2410.21853","title":"Learning Infinitesimal Generators of Continuous Symmetries from Data","created":"2024-10-29","cited_by_count":17,"area":null},{"id":"2409.02431","title":"Adversarial Learning for Neural PDE Solvers with Sparse Data","created":"2024-09-04","cited_by_count":16,"area":null},{"id":"2405.16756","title":"Symmetry-Informed Governing Equation Discovery","created":"2024-05-27","cited_by_count":15,"area":null},{"id":"2403.15989","title":"Knowledge-guided Machine Learning: Current Trends and Future Prospects","created":"2024-03-24","cited_by_count":14,"area":null},{"id":"2110.02083","title":"Applying Machine Learning to Study Fluid Mechanics","created":"2021-10-05","cited_by_count":13,"area":null},{"id":"2209.14991","title":"Machine learning and invariant theory","created":"2022-09-29","cited_by_count":13,"area":null},{"id":"2411.00040","title":"P$^2$C$^2$Net: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamics","created":"2024-10-29","cited_by_count":13,"area":null},{"id":"2102.11218","title":"Neural Pharmacodynamic State Space Modeling","created":"2021-02-22","cited_by_count":12,"area":null},{"id":"2107.12780","title":"Physics-constrained Deep Learning for Robust Inverse ECG Modeling","created":"2021-07-26","cited_by_count":12,"area":null},{"id":"2206.04811","title":"Deep learning-enhanced ensemble-based data assimilation for high-dimensional nonlinear dynamical systems","created":"2022-06-09","cited_by_count":12,"area":null},{"id":"2305.15603","title":"Learning Lagrangian Fluid Mechanics with E($3$)-Equivariant Graph Neural Networks","created":"2023-05-24","cited_by_count":12,"area":null},{"id":"2306.06489","title":"On Robot Grasp Learning Using Equivariant Models","created":"2023-06-10","cited_by_count":12,"area":null},{"id":"2310.05227","title":"Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology","created":"2023-10-08","cited_by_count":11,"area":null},{"id":"2212.00017","title":"Knowledge-augmented Deep Learning and Its Applications: A Survey","created":"2022-11-30","cited_by_count":10,"area":null},{"id":"2305.16614","title":"Physics-Regulated Deep Reinforcement Learning: Invariant Embeddings","created":"2023-05-26","cited_by_count":10,"area":null},{"id":"2308.03312","title":"Exploiting Code Symmetries for Learning Program Semantics","created":"2023-08-07","cited_by_count":10,"area":null},{"id":"2410.05499","title":"Unitary convolutions for learning on graphs and groups","created":"2024-10-07","cited_by_count":8,"area":null},{"id":"2303.16110","title":"Invariant preservation in machine learned PDE solvers via error correction","created":"2023-03-28","cited_by_count":7,"area":null},{"id":"2309.02898","title":"A Unified Framework for Discovering Discrete Symmetries","created":"2023-09-06","cited_by_count":7,"area":null},{"id":"2512.11855","title":"Achieving Approximate Symmetry Is Exponentially Easier than Exact Symmetry","created":"2025-12-05","cited_by_count":7,"area":null},{"id":"2110.03761","title":"A simple equivariant machine learning method for dynamics based on scalars","created":"2021-10-07","cited_by_count":6,"area":null},{"id":"2303.03181","title":"MetaPhysiCa: OOD Robustness in Physics-informed Machine Learning","created":"2023-03-06","cited_by_count":6,"area":null},{"id":"2305.14286","title":"Equivariant Neural Simulators for Stochastic Spatiotemporal Dynamics","created":"2023-05-23","cited_by_count":6,"area":null},{"id":"2505.12083","title":"Discovering Symbolic Differential Equations with Symmetry Invariants","created":"2025-05-17","cited_by_count":6,"area":null},{"id":"2506.05513","title":"Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates","created":"2025-06-05","cited_by_count":6,"area":null},{"id":"2510.01855","title":"Explicit Discovery of Nonlinear Symmetries from Dynamic Data","created":"2025-10-02","cited_by_count":6,"area":null},{"id":"2202.05750","title":"Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning","created":"2022-02-11","cited_by_count":5,"area":null},{"id":"2212.04100","title":"Physics-guided Data Augmentation for Learning the Solution Operator of Linear Differential Equations","created":"2022-12-08","cited_by_count":5,"area":null},{"id":"2306.03228","title":"Discovering Novel Biological Traits From Images Using Phylogeny-Guided Neural Networks","created":"2023-06-05","cited_by_count":5,"area":null},{"id":"2307.05486","title":"Importance of equivariant and invariant symmetries for fluid flow modeling","created":"2023-05-03","cited_by_count":5,"area":null},{"id":"2311.03094","title":"Equivariance Is Not All You Need: Characterizing the Utility of Equivariant Graph Neural Networks for Particle Physics Tasks","created":"2023-11-06","cited_by_count":5,"area":null},{"id":"2412.01297","title":"Morphological-Symmetry-Equivariant Heterogeneous Graph Neural Network for Robotic Dynamics Learning","created":"2024-12-02","cited_by_count":5,"area":null},{"id":"2504.07741","title":"Harnessing Equivariance: Modeling Turbulence with Graph Neural Networks","created":"2025-04-10","cited_by_count":5,"area":null},{"id":"2505.20349","title":"FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulation","created":"2025-05-25","cited_by_count":5,"area":null},{"id":"2410.00435","title":"Incorporating Arbitrary Matrix Group Equivariance into KANs","created":"2024-10-01","cited_by_count":4,"area":null},{"id":"2505.18798","title":"Governing Equation Discovery from Data Based on Differential Invariants","created":"2025-05-24","cited_by_count":4,"area":null},{"id":"2202.11099","title":"Rotationally Equivariant Super-Resolution of Velocity Fields in Two-Dimensional Fluids Using Convolutional Neural Networks","created":"2022-02-22","cited_by_count":3,"area":null},{"id":"2205.07852","title":"REMuS-GNN: A Rotation-Equivariant Model for Simulating Continuum Dynamics","created":"2022-05-05","cited_by_count":3,"area":null},{"id":"2210.06741","title":"Why self-attention is Natural for Sequence-to-Sequence Problems? A Perspective from Symmetries","created":"2022-10-13","cited_by_count":3,"area":null},{"id":"2305.12585","title":"Equivariant geometric convolutions for emulation of dynamical systems","created":"2023-05-21","cited_by_count":3,"area":null},{"id":"2310.19589","title":"Modeling Dynamics over Meshes with Gauge Equivariant Nonlinear Message Passing","created":"2023-10-30","cited_by_count":3,"area":null},{"id":"2406.01552","title":"Tensor learning with orthogonal, Lorentz, and symplectic symmetries","created":"2024-06-03","cited_by_count":3,"area":null},{"id":"2501.15987","title":"MultiPDENet: PDE-embedded Learning with Multi-time-stepping for Accelerated Flow Simulation","created":"2025-01-27","cited_by_count":3,"area":null},{"id":"2505.13569","title":"Surrogate Modeling of 3D Rayleigh-Benard Convection with Equivariant Autoencoders","created":"2025-05-19","cited_by_count":3,"area":null},{"id":"2111.01892","title":"Equivariant Deep Dynamical Model for Motion Prediction","created":"2021-11-02","cited_by_count":2,"area":null},{"id":"2205.01927","title":"Probabilistic Symmetry for Multi-Agent Dynamics","created":"2022-05-04","cited_by_count":2,"area":null},{"id":"2305.00723","title":"Predictions Based on Pixel Data: Insights from PDEs and Finite Differences","created":"2023-05-01","cited_by_count":2,"area":null},{"id":"2309.05352","title":"Neural Discovery of Permutation Subgroups","created":"2023-09-11","cited_by_count":2,"area":null},{"id":"2406.06611","title":"Building Hybrid B-Spline And Neural Network Operators","created":"2024-06-06","cited_by_count":2,"area":null},{"id":"2407.18772","title":"Learning production functions for supply chains with graph neural networks","created":"2024-07-26","cited_by_count":2,"area":null},{"id":"2410.12831","title":"Segment as You Wish -- Free-Form Language-Based Segmentation for Medical Images","created":"2024-10-02","cited_by_count":2,"area":null},{"id":"2502.00373","title":"Generalized Lie Symmetries in Physics-Informed Neural Operators","created":"2025-02-01","cited_by_count":2,"area":null},{"id":"2509.24332","title":"Towards Generalizable PDE Dynamics Forecasting via Physics-Guided Invariant Learning","created":"2025-09-29","cited_by_count":2,"area":null},{"id":"2106.12891","title":"Encoding Involutory Invariances in Neural Networks","created":"2021-06-07","cited_by_count":1,"area":null},{"id":"2112.11656","title":"Latent Space Simulation for Carbon Capture Design Optimization","created":"2021-12-22","cited_by_count":1,"area":null},{"id":"2112.14769","title":"Frame invariance and scalability of neural operators for partial differential equations","created":"2021-12-28","cited_by_count":1,"area":null},{"id":"2202.04109","title":"Learning Similarity Metrics for Volumetric Simulations with Multiscale CNNs","created":"2022-02-08","cited_by_count":1,"area":null},{"id":"2301.06635","title":"Data-aware customization of activation functions reduces neural network error","created":"2023-01-16","cited_by_count":1,"area":null},{"id":"2406.04709","title":"ConDiff: A Challenging Dataset for Neural Solvers of Partial Differential Equations","created":"2024-06-07","cited_by_count":1,"area":null},{"id":"2407.11158","title":"Physics-embedded Fourier Neural Network for Partial Differential Equations","created":"2024-07-15","cited_by_count":1,"area":null},{"id":"2410.15800","title":"On the VC dimension of deep group convolutional neural networks","created":"2024-10-21","cited_by_count":1,"area":null},{"id":"2507.01975","title":"Learnable-Differentiable Finite Volume Solver for Accelerated Simulation of Flows","created":"2025-06-23","cited_by_count":1,"area":null},{"id":"2507.14793","title":"Flow Equivariant Recurrent Neural Networks","created":"2025-07-20","cited_by_count":1,"area":null},{"id":"2507.18813","title":"Scale-Consistent Learning for Partial Differential Equations","created":"2025-07-24","cited_by_count":1,"area":null},{"id":"2510.02683","title":"Can Data-Driven Dynamics Reveal Hidden Physics? There Is A Need for Interpretable Neural Operators","created":"2025-10-03","cited_by_count":1,"area":null}],"next_cursor":"100"}