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Found 38 papers, 7 papers with code
Binned Spectral Power Loss for Improved Prediction of Chaotic Systems
We demonstrate that the BSP loss mitigates the well-known problem of spectral bias in deep learning.
Semi-Implicit Neural Ordinary Differential Equations
Classical neural ODEs trained with explicit methods are intrinsically limited by stability, crippling their efficiency and robustness for stiff learning problems that are common in graph learning and scientific machine learning.
Improved deep learning of chaotic dynamical systems with multistep penalty losses
Predicting the long-term behavior of chaotic systems remains a formidable challenge due to their extreme sensitivity to initial conditions and the inherent limitations of traditional data-driven modeling approaches.
Scalable and Consistent Graph Neural Networks for Distributed Mesh-based Data-driven Modeling
This work develops a distributed graph neural network (GNN) methodology for mesh-based modeling applications using a consistent neural message passing layer.
A competitive baseline for deep learning enhanced data assimilation using conditional Gaussian ensemble Kalman filtering
Ensemble Kalman Filtering (EnKF) is a popular technique for data assimilation, with far ranging applications.
Measure-Theoretic Time-Delay Embedding
The celebrated Takens' embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations.
Mesh-based Super-Resolution of Fluid Flows with Multiscale Graph Neural Networks
To facilitate mesh-based GNN representations in a manner similar to spectral (or finite) element discretizations, a baseline GNN layer (termed a message passing layer, which updates local node properties) is modified to account for synchronization of coincident graph nodes, rendering compatibility with commonly used element-based mesh connectivities.
Higher order quantum reservoir computing for non-intrusive reduced-order models
By mapping the dynamical state to a suitable quantum representation amenable to unitary operations, QRC is able to predict complex nonlinear dynamical systems in a stable and accurate manner.
Divide And Conquer: Learning Chaotic Dynamical Systems With Multistep Penalty Neural Ordinary Differential Equations
In addition to the deviation from the training data, the optimization loss term further penalizes the discontinuities of the predicted trajectory between the time windows.
A note on the error analysis of data-driven closure models for large eddy simulations of turbulence
We also demonstrate that this error is significantly affected by the time step size and the Jacobian which play a role in amplifying the initial one-step error made by using the closure.
LUCIE: A Lightweight Uncoupled ClImate Emulator with long-term stability and physical consistency for O(1000)-member ensembles
We further discuss an improved training strategy with a hard-constrained first-order integrator to suppress autoregressive error growth, a novel spectral regularization strategy to better capture fine-scale dynamics, and finally an optimization algorithm that enables data-limited (as low as $2$ years of $6$-hourly data) training of the emulator without losing stability and physical consistency.
Leveraging Interpolation Models and Error Bounds for Verifiable Scientific Machine Learning
In this work, we present a best-of-both-worlds approach to verifiable scientific machine learning by demonstrating that (1) multiple standard interpolation techniques have informative error bounds that can be computed or estimated efficiently; (2) comparative performance among distinct interpolants can aid in validation goals; (3) deploying interpolation methods on latent spaces generated by deep learning techniques enables some interpretability for black-box models.
Data-Driven Physics-Informed Neural Networks: A Digital Twin Perspective
This study explores the potential of physics-informed neural networks (PINNs) for the realization of digital twins (DT) from various perspectives.
Scaling transformer neural networks for skillful and reliable medium-range weather forecasting
At the core of Stormer is a randomized forecasting objective that trains the model to forecast the weather dynamics over varying time intervals.
Interpretable A-posteriori Error Indication for Graph Neural Network Surrogate Models
Data-driven surrogate modeling has surged in capability in recent years with the emergence of graph neural networks (GNNs), which can operate directly on mesh-based representations of data.
DeepSpeed4Science Initiative: Enabling Large-Scale Scientific Discovery through Sophisticated AI System Technologies
In the upcoming decade, deep learning may revolutionize the natural sciences, enhancing our capacity to model and predict natural occurrences.
Robust experimental data assimilation for the Spalart-Allmaras turbulence model
This calibration relies on the assimilation of experimental data collected in the form of velocity profiles, skin friction, and pressure coefficients.
Generalizable data-driven turbulence closure modeling on unstructured grids with differentiable physics
Our end-to-end learning paradigm demonstrates a viable pathway for physically consistent and generalizable data-driven closure modeling across complex geometries.
Differentiable Turbulence: Closure as a partial differential equation constrained optimization
Deep learning is increasingly becoming a promising pathway to improving the accuracy of sub-grid scale (SGS) turbulence closure models for large eddy simulations (LES).
Importance of equivariant and invariant symmetries for fluid flow modeling
Graph neural networks (GNNs) have shown promise in learning unstructured mesh-based simulations of physical systems, including fluid dynamics.
Generative modeling of time-dependent densities via optimal transport and projection pursuit
Motivated by the computational difficulties incurred by popular deep learning algorithms for the generative modeling of temporal densities, we propose a cheap alternative which requires minimal hyperparameter tuning and scales favorably to high dimensional problems.
Quantifying uncertainty for deep learning based forecasting and flow-reconstruction using neural architecture search ensembles
We demonstrate the feasibility of this framework for two tasks - forecasting from historical data and flow reconstruction from sparse sensors for the sea-surface temperature.
Multiscale Graph Neural Network Autoencoders for Interpretable Scientific Machine Learning
The goal of this work is to address two limitations in autoencoder-based models: latent space interpretability and compatibility with unstructured meshes.
Differentiable physics-enabled closure modeling for Burgers' turbulence
Data-driven turbulence modeling is experiencing a surge in interest following algorithmic and hardware developments in the data sciences.
Stabilized Neural Ordinary Differential Equations for Long-Time Forecasting of Dynamical Systems
We present a data-driven modeling method that accurately captures shocks and chaotic dynamics by proposing a novel architecture, stabilized neural ordinary differential equation (ODE).
Multi-fidelity reinforcement learning framework for shape optimization
One key limitation of conventional DRL methods is their episode-hungry nature which proves to be a bottleneck for tasks which involve costly evaluations of a numerical forward model.
AutoDEUQ: Automated Deep Ensemble with Uncertainty Quantification
However, building ensembles of neural networks is a challenging task because, in addition to choosing the right neural architecture or hyperparameters for each member of the ensemble, there is an added cost of training each model.
Assessments of epistemic uncertainty using Gaussian stochastic weight averaging for fluid-flow regression
The average of such an ensemble can be regarded as the `mean estimation', whereas its standard deviation can be used to construct `confidence intervals', which enable us to perform uncertainty quantification (UQ) with regard to the training process of neural networks.
Data-Driven Wind Turbine Wake Modeling via Probabilistic Machine Learning
Physics-based models that capture the wake flow-field with high-fidelity are computationally very expensive to perform layout optimization of wind farms, and, thus, data-driven reduced order models can represent an efficient alternative for simulating wind farms.
Learning the temporal evolution of multivariate densities via normalizing flows
Specifically, the learned map is a multivariate normalizing flow that deforms the support of the reference density to the support of each and every density snapshot in time.
Data-driven geophysical forecasting: Simple, low-cost, and accurate baselines with kernel methods
Modeling geophysical processes as low-dimensional dynamical systems and regressing their vector field from data is a promising approach for learning emulators of such systems.
Global field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learning
This reconstruction problem is especially difficult when sensors are sparsely positioned in a seemingly random or unorganized manner, which is often encountered in a range of scientific and engineering problems.
Deploying deep learning in OpenFOAM with TensorFlow
We outline the development of a data science module within OpenFOAM which allows for the in-situ deployment of trained deep learning architectures for general-purpose predictive tasks.
Meta-modeling strategy for data-driven forecasting
Accurately forecasting the weather is a key requirement for climate change mitigation.
Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation
We assess the viability of this algorithm for an advection-dominated system given by the inviscid shallow water equations.
Probabilistic neural networks for fluid flow surrogate modeling and data recovery
We consider the use of probabilistic neural networks for fluid flow surrogate modeling and data recovery.
Fluid Dynamics
Using recurrent neural networks for nonlinear component computation in advection-dominated reduced-order models
Rapid simulations of advection-dominated problems are vital for multiple engineering and geophysical applications.
Site-specific graph neural network for predicting protonation energy of oxygenate molecules
These oxygenated molecules have adequate carbon, hydrogen, and oxygen atoms that can be used for developing new value-added molecules (chemicals or transportation fuels).
