We study first-order optimization methods obtained by discretizing ordinary differential equations (ODEs) corresponding to Nesterov's accelerated gradient methods (NAGs) and Polyak's heavy-ball method. We consider three discretization schemes: an explicit Euler scheme, an implicit Euler scheme, and a symplectic scheme.…
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48 results for “High-Resolution Differential Equations”
Last-Iterate Convergence of Saddle-Point Optimizers via High-Resolution Differential Equationsmath.OC
New ODE models show saddle-point optimization methods converge differently, with last-iterate convergence for OGDA.
problem Analyzing convergence properties of saddle-point optimization methods.
method High-Resolution Differential Equations (HRDEs) to design differential equation models for saddle-point optimization methods.
result HRDEs reveal last-iterate convergence for Optimistic Gradient Descent Ascent (OGDA) in bilinear games.
Gradient-based optimization algorithms can be studied from the perspective of limiting ordinary differential equations (ODEs). Motivated by the fact that existing ODEs do not distinguish between two fundamentally different algorithms---Nesterov's accelerated gradient method for strongly convex functions (NAG-SC) and Po…
Transforms game optimization dynamics into frequency domain for precise hyperparameter analysis.
problem Analyzing convergence of hyperparameters in game optimization.
method Frequency-domain framework using High-Resolution Differential Equations (HRDEs) and Laplace transforms.
result Derives precise convergence criteria for the Lookahead algorithm.
Image compression is an essential approach for decreasing the size in bytes of the image without deteriorating the quality of it. Typically, classic algorithms are used but recently deep-learning has been successfully applied. In this work, is presented a deep super-resolution work-flow for image compression that maps …
Efficiently processes high res images by selecting relevant patches.
problem High memory and compute requirements for processing large images.
method Differentiable Top-K operator to select relevant patches.
result End-to-end trainable model using backpropagation.
MeshfreeFlowNet generates high-resolution spatio-temporal solutions from low-resolution inputs.
problem Generating high-resolution spatio-temporal solutions from low-resolution inputs.
method Physics-constrained deep learning framework using fully convolutional encoders.
result Significantly outperforms existing baselines in super-resolution of turbulent flows.
Physically-Inspired Gaussian Process Models for Post-Transcriptional Regulation in Drosophilastat.ML
The regulatory process of Drosophila is thoroughly studied for understanding a great variety of biological principles. While pattern-forming gene networks are analysed in the transcription step, post-transcriptional events (e.g. translation, protein processing) play an important role in establishing protein expression …
Modeling wind dynamics in Saudi Arabia using deep learning and stochastic PDEs.
problem Accurately modeling spatio-temporal wind patterns in a large, diverse, and understudied region.
method Energy distance-based spatial reduction, sparse stochastic Echo State Network, non-stationary stochastic PDE reconstruction.
result Produces more accurate wind speed and energy forecasts, saving $1 million annually.
Cut-DeepONet handles discontinuities and sharp transitions in neural operators.
problem Neural operators struggle with discontinuities and sharp transitions in PDEs.
method Two-stage training framework that explicitly models discontinuities via a lifting strategy and input-dependent discontinuity prediction.
result Cut-DeepONet outperforms state-of-the-art methods on benchmark PDEs with low-resolution datasets.
This paper simplifies diffusion models for high resolution images.
problem Applying diffusion models to high resolution images is challenging.
method Adjust noise schedule, scale specific parts, add dropout, and use downsampling.
result Achieved state-of-the-art image generation performance.
Researchers use operator learning to predict cardiac activation and repolarization times.
problem Computational demands and need for clear, interpretable information in cardiac electrophysiology.
method Exploiting Fourier Neural Operators (FNO) and Kernel Operator Learning (KOL) to learn operator mappings.
result Both FNO and KOL approaches are computationally efficient and robust to hyperparameters.
Coupled continuous time random walks in financephysics.data-an
Continuous time random walks (CTRWs) are used in physics to model anomalous diffusion, by incorporating a random waiting time between particle jumps. In finance, the particle jumps are log-returns and the waiting times measure delay between transactions. These two random variables (log-return and waiting time) are typi…
StyleNeRF generates high-resolution images with 3D consistency and style control.
problem Generating high-resolution images with fine details and 3D consistency.
method Integrates NeRF into a style-based generator for efficient high-resolution image synthesis.
result Synthesizes high-resolution images at interactive rates with high 3D consistency and style control.
Method fuses low and high-resolution data for better health estimates.
problem Improving high-resolution health estimates from mixed data sources.
method Fusion of unbiased low-resolution and potentially biased high-resolution data, learning a distribution consistent with sampling bias.
result Significant reduction in bias in high-resolution estimates.
Mapping Low-Resolution Images To Multiple High-Resolution Images Using Non-Adversarial Mappingeess.IV
SR-NAM maps low-res images to multiple high-res images realistically.
problem Mapping low-resolution images to multiple high-resolution images realistically.
method SR-NAM using Non-Adversarial Mapping (NAM) technique and a degradation model.
result Realistic degradation and down-sampling of high-resolution images.
The shortage of high-resolution urban digital elevation model (DEM) datasets has been a challenge for modelling urban flood and managing its risk. A solution is to develop effective approaches to reconstruct high-resolution DEMs from their low-resolution equivalents that are more widely available. However, the current …
High-resolution signal recovery via generalized sampling and functional principal component analysismath.ST
The paper presents a method to recover high-resolution signals from low-resolution measurements.
problem Recovering high-resolution signals from low-resolution indirect measurements.
method Combining generalized sampling and functional principal component analysis.
result High-resolution recovery is possible under certain conditions and with a sufficiently large training set.
Pixel-space diffusion models outperform latent models on high-resolution image synthesis.
problem Efficiency and quality trade-off in high-resolution image synthesis.
method Sigmoid loss-weighting, simplified architecture, and resolution scaling.
result Achieved 1.5 FID on ImageNet512, new SOTA results on other datasets.
Training a deep neural network for classification constitutes a major problem in remote sensing due to the lack of adequate field data. Acquiring high-resolution ground truth (GT) by human interpretation is both cost-ineffective and inconsistent. We propose, instead, to utilize high-resolution, hyperspectral images for…
We present a method of generating high resolution 3D shapes from natural language descriptions. To achieve this goal, we propose two steps that generating low resolution shapes which roughly reflect texts and generating high resolution shapes which reflect the detail of texts. In a previous paper, the authors have show…
UNSB uses neural Schrödinger Bridge to solve unpaired image-to-image translation.
problem Difficulties in unpaired image-to-image translation with diffusion models.
method Expresses SB problem as adversarial learning problems, incorporating advanced discriminators and regularization.
result Successfully solves various unpaired image-to-image translation tasks.
We propose Progressive Structure-conditional Generative Adversarial Networks (PSGAN), a new framework that can generate full-body and high-resolution character images based on structural information. Recent progress in generative adversarial networks with progressive training has made it possible to generate high-resol…
Obtaining magnetic resonance images (MRI) with high resolution and generating quantitative image-based biomarkers for assessing tissue biochemistry is crucial in clinical and research applications. How- ever, acquiring quantitative biomarkers requires high signal-to-noise ratio (SNR), which is at odds with high-resolut…
High-Resolution Peak Demand Estimation Using Generalized Additive Models and Deep Neural Networkscs.LG
Paper proposes combining GAM and DNN for accurate peak demand estimation from lower-resolution data.
problem Predicting high-resolution peak demand from limited lower-resolution data.
method Combines generalized additive models (GAM) and deep neural networks (DNN) for half-hourly load forecasting.
result Proposed method reduces out-of-sample RMSE by 57.4% compared to benchmark.
Climate projections continue to be marred by large uncertainties, which originate in processes that need to be parameterized, such as clouds, convection, and ecosystems. But rapid progress is now within reach. New computational tools and methods from data assimilation and machine learning make it possible to integrate …
Background: Three-dimensional, whole heart, balanced steady state free precession (WH-bSSFP) sequences provide delineation of intra-cardiac and vascular anatomy. However, they have long acquisition times. Here, we propose significant speed ups using a deep learning single volume super resolution reconstruction, to reco…
Deep learning upscales geologic models efficiently.
problem Upscaling large-scale geologic models for efficient simulation.
method Theory-guided convolutional neural network (TgCNN) trained to approximate hydraulic conductivity relationships.
result Deep learning method achieves equivalent upscaling accuracy to numerical methods but with significantly improved efficiency.
This research accelerates sampling methods using Nesterov's Acceleration.
problem Improving sampling efficiency in MCMC methods.
method Developed a Hessian-Free High-Resolution ODE reformulation of NAG-SC, injected noise, and discretized the diffusion process.
result Quantified acceleration beyond underdamped Langevin in distance for log-strongly-concave targets.
Studies projective geometry and partial differential equations prolongation.
problem Understanding the prolongation of overdetermined geometric partial differential equations.
method Introduction to differential geometry and tractor calculus, study of prolongation of equations.
result Recovery of projective tractor and cotractor connections via partial differential equations prolongation.
Paper solves a class of differential equations with specific solutions.
problem Identifying solutions to a class of nonlinear ODEs.
method Solves using a proposed side condition involving a third-order linear ODE.
result New closed and integral-form solutions for the Tzitzeica curve equation.
We analyze high-resolution foreign exchange data consisting of 20 million data points of USD-JPY for 13 years to report firm statistical laws in distributions and correlations of exchange rate fluctuations. A conditional probability density analysis clearly shows the existence of trend-following movements at time scale…
CESAR improves wind speed and power forecasting for high-resolution simulations.
problem Accurate high-resolution wind forecasting for efficient power grid management.
method A spatio-temporal neural network model using deep convolutional autoencoder and echo state network.
result CESAR provides up to 17% improvement in wind speed and power forecasting compared to best alternatives.
Running high-resolution physical models is computationally expensive and essential for many disciplines. Agriculture, transportation, and energy are sectors that depend on high-resolution weather models, which typically consume many hours of large High Performance Computing (HPC) systems to deliver timely results. Many…
The paper generalizes Monge-Ampère equations and their solutions in differential geometry.
problem Understanding the structure of Monge-Ampère equations and their solutions.
method Generalizing Monge-Ampère equations to higher-order systems and proving their solutions correspond to integral manifolds of exterior differential systems.
result The Korteweg-de Vries (KdV) equation and Cauchy-Riemann equations are examples of generalized Monge-Ampère equations.
DiffEqFlux.jl is a library for fusing neural networks and differential equations. In this work we describe differential equations from the viewpoint of data science and discuss the complementary nature between machine learning models and differential equations. We demonstrate the ability to incorporate DifferentialEqua…
Classifies scalar second-order PDEs with low-dimensional symmetry groups.
problem Classifying differential equations with specific symmetry groups.
method Algebraic technique based on covariant form for constructing equations.
result Complete classification of quasi-linear scalar second-order PDEs with free symmetry groups of dimension ≤3.
New method models PDEs from noisy, limited data.
problem Modeling PDEs with incomplete, noisy data.
method Learned linear transformation of spatial grid points, followed by dynamics learning in a reduced basis, then back transformation.
result Rapid high-resolution simulations with smaller training data sets.
Neural differential equations combine deep learning and differential equations for modeling complex systems.
problem Modeling complex systems with high capacity and efficiency.
method Combining neural networks and differential equations, focusing on neural ordinary, controlled, and stochastic differential equations.
result NDEs offer high-capacity function approximation, strong priors, and handle irregular data efficiently.
Neural networks can approximate complex stochastic equations well.
problem Approximating general stochastic differential equations.
method Identified neural network classes approximating continuous functions.
result Neural stochastic differential equations can approximate general stochastic differential equations arbitrarily well.
Engine predicts real-time air quality with high resolution.
problem Real-time prediction of air pollutants for health monitoring.
method Combines official data, models, land cover, traffic data for high-resolution predictions.
result Engine produces predictions with resolution of a few dozen meters.
New method solves PDEs for any initial condition without retraining.
problem Solving PDEs for different initial conditions requires retraining neural solvers.
method Formulate solution as conditional probability distribution.
result Approximates PDE solution for arbitrary initial conditions.
Paper discovers governing equations from data using differential invariants.
problem Discovering partial differential equations from data is challenging.
method The paper proposes a pipeline based on differential invariants to reduce the search space and adhere to symmetry.
result DI-SINDy method outperforms other symmetry-informed methods in PDE discovery.
Stochastic Partial Differential Equations on Evolving Surfaces and Evolving Riemannian Manifoldsmath.AP
We formulate stochastic partial differential equations on Riemannian manifolds, moving surfaces, general evolving Riemannian manifolds (with appropriate assumptions) and Riemannian manifolds with random metrics, in the variational setting of the analysis to stochastic partial differential equations. Considering mainly …
New variational principle found for non-variational differential equations.
problem Non-variational differential equations without variational multipliers.
method Connecting functional forms with antiexact differential forms to identify obstructions.
result Formulation of variational problem for non-variational equations.
Developed a theory of local convexity for second order differential equations on Lie algebroids.
problem Analyzing convexity in differential equations on Lie algebroids.
method Theory development for local convexity of SODEs on Lie algebroids.
result Extensive discussion of homogeneous quadratic SODEs on Lie algebroids.
Differentiable programming aids in solving differential equations and their sensitivities.
problem Computing gradients of numerical solutions of differential equations.
method Review of existing techniques and mathematical foundations.
result Established a coherent framework for combining differential equations with data-driven approaches.
The theory of Lie remarkable equations, i.e. differential equations characterized by their Lie point symmetries, is reviewed and applied to ordinary differential equations. In particular, we consider some relevant Lie algebras of vector fields on and characterize Lie remarkable equations admitted by the …