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Found 30 papers, 7 papers with code
Understanding and Mitigating Membership Inference Risks of Neural Ordinary Differential Equations
By accurately learning underlying dynamics in data in the form of differential equations, NODEs have been widely adopted in various domains, such as healthcare, finance, computer vision, and language modeling.
Physics-informed reduced order model with conditional neural fields
This study presents the conditional neural fields for reduced-order modeling (CNF-ROM) framework to approximate solutions of parametrized partial differential equations (PDEs).
MaD-Scientist: AI-based Scientist solving Convection-Diffusion-Reaction Equations Using Massive PINN-Based Prior Data
Large language models (LLMs), like ChatGPT, have shown that even trained with noisy prior data, they can generalize effectively to new tasks through in-context learning (ICL) and pre-training techniques.
FastLRNR and Sparse Physics Informed Backpropagation
We introduce Sparse Physics Informed Backpropagation (SPInProp), a new class of methods for accelerating backpropagation for a specialized neural network architecture called Low Rank Neural Representation (LRNR).
Latent Space Energy-based Neural ODEs
This family of models generates each data point in the time series by a neural emission model, which is a non-linear transformation of a latent state vector.
Parameterized Physics-informed Neural Networks for Parameterized PDEs
Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Reynolds number in fluid mechanics.
Efficiently Parameterized Neural Metriplectic Systems
Metriplectic systems are learned from data in a way that scales quadratically in both the size of the state and the rank of the metriplectic data.
PAC-FNO: Parallel-Structured All-Component Fourier Neural Operators for Recognizing Low-Quality Images
Extensively evaluating methods with seven image recognition benchmarks, we show that the proposed PAC-FNO improves the performance of existing baseline models on images with various resolutions by up to 77. 1% and various types of natural variations in the images at inference.
Learning Flexible Body Collision Dynamics with Hierarchical Contact Mesh Transformer
These methods are typically designed to i) reduce the computational cost in solving physical dynamics and/or ii) propose techniques to enhance the solution accuracy in fluid and rigid body dynamics.
Ranked #1 on
Physical Simulations
on Deformable Plate
Operator-learning-inspired Modeling of Neural Ordinary Differential Equations
Neural ordinary differential equations (NODEs), one of the most influential works of the differential equation-based deep learning, are to continuously generalize residual networks and opened a new field.
Graph Convolutions Enrich the Self-Attention in Transformers!
We propose a graph-filter-based self-attention (GFSA) to learn a general yet effective one, whose complexity, however, is slightly larger than that of the original self-attention mechanism.
Ranked #1 on
Speech Recognition
on LibriSpeech 100h test-other
Reversible and irreversible bracket-based dynamics for deep graph neural networks
Recent works have shown that physics-inspired architectures allow the training of deep graph neural networks (GNNs) without oversmoothing.
Climate modeling with neural advection–diffusion equation
Owing to the remarkable development of deep learning technology, there have been a series of efforts to build deep learning-based climate models.
Time Series Forecasting with Hypernetworks Generating Parameters in Advance
Forecasting future outcomes from recent time series data is not easy, especially when the future data are different from the past (i. e. time series are under temporal drifts).
Mining Causality from Continuous-time Dynamics Models: An Application to Tsunami Forecasting
However, parameterization of dynamics using a neural network makes it difficult for humans to identify causal structures in the data.
Parameter-varying neural ordinary differential equations with partition-of-unity networks
In this study, we propose parameter-varying neural ordinary differential equations (NODEs) where the evolution of model parameters is represented by partition-of-unity networks (POUNets), a mixture of experts architecture.
AdamNODEs: When Neural ODE Meets Adaptive Moment Estimation
In this work, we propose adaptive momentum estimation neural ODEs (AdamNODEs) that adaptively control the acceleration of the classical momentum-based approach.
Unsupervised physics-informed disentanglement of multimodal data for high-throughput scientific discovery
We introduce physics-informed multimodal autoencoders (PIMA) - a variational inference framework for discovering shared information in multimodal scientific datasets representative of high-throughput testing.
Climate Modeling with Neural Diffusion Equations
On the other hand, neural ordinary differential equations (NODEs) are to learn a latent governing equation of ODE from data.
Regularizing Image Classification Neural Networks with Partial Differential Equations
In other words, the knowledge contained by the learned governing equation can be injected into the neural network which approximates the PDE solution function.
Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling
Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved forecasting, stability, and physical realizability guarantees.
Probabilistic partition of unity networks: clustering based deep approximation
We enrich POU-Nets with a Gaussian noise model to obtain a probabilistic generalization amenable to gradient-based minimization of a maximum likelihood loss.
Machine learning structure preserving brackets for forecasting irreversible processes
Forecasting of time-series data requires imposition of inductive biases to obtain predictive extrapolation, and recent works have imposed Hamiltonian/Lagrangian form to preserve structure for systems with reversible dynamics.
Partition of unity networks: deep hp-approximation
Approximation theorists have established best-in-class optimal approximation rates of deep neural networks by utilizing their ability to simultaneously emulate partitions of unity and monomials.
Neural Partial Differential Equations
Neural ordinary differential equations (neural ODEs) introduced an approach to approximate a neural network as a system of ODEs after considering its layer as a continuous variable and discretizing its hidden dimension.
DPM: A Novel Training Method for Physics-Informed Neural Networks in Extrapolation
We present a method for learning dynamics of complex physical processes described by time-dependent nonlinear partial differential equations (PDEs).
Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems
This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs.
Deep Conservation: A latent dynamics model for exact satisfaction of physical conservation laws
In contrast to existing methods for latent dynamics learning, this is the only method that both employs a nonlinear embedding and computes dynamics for the latent state that guarantee the satisfaction of prescribed physical properties.
Computational Physics
Solving Large-Scale 0-1 Knapsack Problems and its Application to Point Cloud Resampling
0-1 knapsack is of fundamental importance in computer science, business, operations research, etc.
MMGAN: Manifold Matching Generative Adversarial Network
MMGAN finds two manifolds representing the vector representations of real and fake images.
