The study focuses on estimating and predicting time-varying origin to destination (OD) trip tables for a dynamic traffic assignment (DTA) model. A bi-level optimisation problem is formulated and solved to estimate OD flows from pre-existent demand matrix and historical traffic flow counts. The estimated demand is then …
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48 results for “OD flow prediction”
Bayesian Gaussian Process ODEs enhanced with normalizing flows for improved flexibility and accuracy.
problem Limitations of standard Gaussian Process ODEs in modeling complex scenarios.
method Introducing normalizing flows to reparameterize the ODE vector field, developing a data-driven variational learning algorithm.
result Improved accuracy and uncertainty estimates for Bayesian Gaussian Process ODEs.
OpFlow predicts robust OD flows by learning choice potentials conditioned on spatial exposures.
problem Deep models trained on raw counts are vulnerable to distribution shift.
method OpFlow learns row-centered choice potentials and reconstructs flows by combining them with a calibrated origin scale.
result OpFlow improves robustness under environment shifts, as shown by controlled synthetic shifts and a real-world experiment.
The paper provides convergence guarantees for ODE-based generative models using transformers.
problem Theoretical guarantees for ODE-based generative models.
method A pre-trained autoencoder maps inputs to a latent space, and a transformer predicts the velocity field.
result The distribution of samples generated via estimated ODE flow converges to the target distribution in Wasserstein-2 distance.
StAD predicts divergence of diffusion and flow models without Jacobian computation.
problem Computing likelihood from diffusion and flow models is computationally expensive.
method Introduces StAD, a distillation method to predict divergence using Langevin-Stein operator.
result StAD predicts divergence with competitive variance and speed compared to existing methods.
Convergence Analysis for General Probability Flow ODEs of Diffusion Models in Wasserstein Distancesstat.ML
Paper analyzes convergence of ODE samplers in Wasserstein distances.
problem Limited theoretical understanding of convergence properties of probability flow ODEs.
method Convergence analysis for general probability flow ODEs in 2-Wasserstein distance.
result First non-asymptotic convergence analysis for probability flow ODE samplers.
The paper improves the probability flow ODE sampler for faster sampling of natural images.
problem Improving the convergence rate of the probability flow ODE sampler.
method Adapting the probability flow ODE sampler to exploit intrinsic low-dimensional structures in natural image data.
result Achieves a dimension-free convergence rate of in total variation distance, improving upon existing results.
A new ODE model explains gradient descent dynamics near edge of stability.
problem Understanding gradient-based training over non-convex landscapes.
method Rod Flow, a new ODE approximation of GD dynamics.
result Rod Flow accurately predicts critical sharpness threshold and self-stabilization in quartic potentials.
An Ode to an ODEcs.LG
New paradigm for Neural ODEs stabilizes training and improves model performance.
problem Gradient vanishing-explosion problem in training deep neural networks.
method ODEtoODE: Nested system of flows with orthogonal group constraints.
result Strong convergence results and improved downstream models in reinforcement learning and supervised learning.
Hypersolvers enable fast continuous-depth models for practical applications.
problem Infinite-depth models like Neural ODEs are computationally infeasible for large problems.
method Introducing hypersolvers, neural networks that solve ODEs efficiently with theoretical guarantees.
result Hypersolvers achieve comparable inference time to traditional discrete networks, making continuous-depth models practical.
A new method for sampling from complex distributions using Langevin samplers.
problem Sampling from unnormalized Boltzmann densities.
method Probability flow ODE derived from linear stochastic interpolants, employing Langevin samplers.
result Efficient simulation of the flow with non-asymptotic convergence rate.
Derives PF-ODE for infinite-dimensional functions, improving function generation tasks.
problem Efficient inference in infinite-dimensional diffusion models.
method Derives PF-ODE in infinite-dimensional function spaces.
result Reduces function evaluations while maintaining sample quality.
New error bounds for flow matching methods using deterministic sampling.
problem Improving the accuracy of flow matching methods for generating probability distributions.
method Derived error bounds for flow matching methods under deterministic sampling conditions.
result Presented error bounds for flow matching methods using loss and regularity conditions.
Neural ODEs extended to manifolds for flexible sampling.
problem Sampling from complex multimodal distributions on non-trivial topologies.
method Extending Neural ODEs to smooth manifolds using vector fields.
result A general methodology for building normalizing flows on manifolds.
A new method for learning conditional distributions using ODEs and neural networks.
problem Learning conditional distributions efficiently and accurately.
method Conditional Föllmer Flow, discretized with Euler's method, using nonparametric velocity estimation.
result Effective approximation of target conditional distributions, with convergence results for Wasserstein-2 distance.
Bi-Lipschitz flows approximate a wide range of distributions.
problem Characterizing the expressivity of bi-Lipschitz normalizing flows.
method Linking score regularity to transport map bi-Lipschitzness via probability flow ODE.
result Gaussian pullbacks induced by bi-Lipschitz variance-preserving transport maps are -dense among all probability densities.
Flow-based models use ODEs to generate complex data distributions.
problem Generating high-dimensional data with complex probability distributions.
method Flow-based models use invertible mappings governed by ODEs to capture these distributions.
result Flow-based models provide exact likelihood estimation and efficient sampling.
New method speeds up generative modeling without requiring diffusion steps.
problem Improving the speed and efficiency of generative modeling techniques.
method Probability flow ODE with a corrector step, achieving better dimension dependence.
result Better dimension dependence ( vs. , assuming smoothness of the data distribution).
Deep residual networks implicitly converge to neural ODEs.
problem Link between discrete and continuous deep learning models.
method Establishing implicit regularization for residual networks towards neural ODEs.
result Deep residual networks initialized as discretizations of neural ODEs converge to such ODEs during training.
SeqRF straightens generative model flows to speed up sampling.
problem High global truncation error in ODE-based solvers for generative models.
method SeqRF, a learning technique that straightens the probability flow.
result Significantly improved sampling speed and synthesis quality.
In the vector space of algebraic curvature operators we study the reaction ODE $$\frac{dR}{dt} = R^2+R^{#}= Q(R)$$ which is associated to the evolution equation of the Riemann curvature oper- ator along the Ricci flow. More precisely, we analyze the stability of a special class of zeros of this ODE up to suitable norma…
New bounds for generative models under weaker assumptions.
problem Establishing convergence guarantees for generative models under weak assumptions.
method Non-asymptotic 2-Wasserstein distance bounds for probability flow ODEs under weak log-concavity and Lipschitz continuity.
result Concrete convergence rates for generative models, including non-log-concave distributions.
Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated quantification of prediction uncertainty, while maintaining the expressive power …
New theory improves diffusion model convergence for generating data.
problem Improving convergence of diffusion models for data generation.
method Developed a non-asymptotic convergence theory for probability flow ODEs.
result Proves iterations suffice for approximating target distributions.
Neural ODEs' performance varies with numerical method, requiring adaptive step size control.
problem Neural ODEs' performance depends on the numerical method used during training.
method Proposes an adaptive step size control algorithm to ensure a valid ODE without increasing computational cost.
result Valid Neural ODEs require careful numerical method selection and step size adaptation.
Neural Manifold ODEs improve manifold data modeling.
problem Adapting deep generative models to non-Euclidean spaces.
method Introducing Neural Manifold ODEs for manifold generalization and continuous probability computation.
result Improves density estimation and downstream tasks on arbitrary manifolds.
This paper compares two methods for training neural ODEs in time-series regression and CNFs.
problem Training neural ODEs for time-series regression and CNFs efficiently.
method Discretize-Optimize (Disc-Opt) vs. Optimize-Discretize (Opt-Disc) approaches.
result Disc-Opt methods can achieve similar performance as Opt-Disc at inference with drastically reduced training costs.
We accelerate CNF by reducing ODE truncation errors with polynomial regularization.
problem High computation cost of CNF due to large truncation errors in solving ODEs.
method Add polynomial regularization to approximate ODE trajectories with polynomial functions.
result 42.3% to 71.3% reduction of NFE on density estimation, 19.3% to 32.1% on variational auto-encoder.
Augmented Normalizing Flows: Bridging the Gap Between Generative Flows and Latent Variable Modelscs.LG
Enhances generative models by improving expressivity without high computational cost.
problem Improving expressivity in generative models without increasing computational complexity.
method Proposes a new family of generative flows on an augmented data space, proving they can approximate a Hamiltonian ODE as a universal transport map.
result Demonstrates state-of-the-art performance on flow-based generative modeling benchmarks.
Paper proves higher-order flow matching preserves optimality in generative modeling.
problem Theoretical guarantees for higher-order flow matching in generative modeling.
method Neural network approximations with controlled depth, width, and sparsity.
result Proves worst case optimality for second-order flow matching.
A functional central limit theorem for kernel gradient flow and infinitesimal gradient boostingmath.PR
Functional central limit theorem for kernel gradient flow and infinitesimal gradient boosting
problem Fluctuations of boosting processes around their deterministic limit
method Stochastic perturbation analysis of ODEs in Banach spaces
result Rescaled deviations converge to a Gaussian process
Enhanced Neural ODEs outperform traditional models in image classification and video prediction.
problem Efficiently modeling time-varying dynamics in neural networks.
method Proposed a novel family of non-autonomous Neural ODEs with time-varying weights.
result Outperformed previous Neural ODE variants in speed and representational capacity.
JKO-iFlow uses neural ODEs to improve generative models with reduced memory and training complexity.
problem Efficiently training deep generative models in high dimensions with reduced memory and training complexity.
method JKO scheme inspired neural ODE flow network with adaptive time reparameterization.
result JKO-iFlow achieves competitive performance compared to existing models at reduced computational and memory cost.
Higher-order ODE solvers improve deep learning performance.
problem Improving deep learning performance using higher-order ODE solvers.
method Evaluation and improvement of Runge-Kutta (RK) methods for deep learning.
result Higher-order RK solvers can improve deep learning performance by incorporating key ingredients of optimizers.
Improved neural ODEs learn adaptable flows.
problem Neural ODEs struggle with expressive power and adaptability.
method Introduce N-CODE modules with dynamic parameters controlled by a trainable map.
result N-CODE modules enhance expressivity of neural ODEs.
Neural ordinary differential equations (ODEs) have been attracting increasing attention in various research domains recently. There have been some works studying optimization issues and approximation capabilities of neural ODEs, but their robustness is still yet unclear. In this work, we fill this important gap by expl…
New method sparsifies hybrid neural ODEs for better performance and stability.
problem Excessive latent states and interactions from mechanistic models lead to training inefficiency and over-fitting.
method Automatic state selection and structure optimization combining domain-informed graph modifications with data-driven regularization.
result Improved predictive performance and robustness with desired sparsity.
Efficiently trains forward processes to minimize generative trajectories curvature.
problem High curvature of generative trajectories slows down sampling speed.
method Trains forward process to minimize curvature without ODE/SDE simulation.
result Lower curvature than previous models, decreased sampling costs.
Neural Jump Ordinary Differential Equations: Consistent Continuous-Time Prediction and Filteringstat.ML
Neural Jump ODE improves continuous-time prediction and filtering of irregularly sampled time series.
problem Theoretical guarantees for continuous-time prediction and filtering of irregularly observed time series.
method Introducing Neural Jump ODE (NJ-ODE) that models conditional expectation between observations with neural ODEs and jumps.
result Theoretical guarantees for the -optimal prediction are provided, showing convergence of model output to optimal prediction.
New algorithm classifies and generates genomic sequences using RG-flow categorifier.
problem Classifying and generating genomic sequences for disease prediction.
method RG-flow based categorifier combining quantum field theory, holographic duality, and neural ODEs.
result RG categorifier can classify and generate new sequences from genomic data.
Paper develops a generative model using Wasserstein-2 loss.
problem Creating realistic data samples from limited data.
method Uses a distribution-dependent ODE with a gradient flow for W2 loss.
result The method converges to the true data distribution exponentially.
We extend rectified flow to infinite-dimensional Hilbert space.
problem Extending rectified flow to infinite-dimensional spaces.
method Established a rigorous functional formulation using the superposition principle for continuity equations.
result Demonstrated superior performance compared to existing models.
We present a particle flow realization of Bayes' rule, where an ODE-based neural operator is used to transport particles from a prior to its posterior after a new observation. We prove that such an ODE operator exists. Its neural parameterization can be trained in a meta-learning framework, allowing this operator to re…
OT-Flow uses optimal transport to improve CNFs for faster and more accurate density estimation.
problem Computational challenges in continuous normalizing flows.
method OT-Flow leverages optimal transport to regularize CNFs and uses exact trace computation.
result OT-Flow achieves competitive performance with one-fourth the number of weights and significant speedups.
A simple regularization technique speeds up training of Neural ODEs.
problem Training Neural ODEs is computationally expensive.
method Randomly sampling the end time of the ODE during training.
result Significantly decreases training time and improves performance.
A new Fourier model improves ODE prediction.
problem Improving the accuracy of ODE solutions, especially for periodic functions.
method Constructing a Fourier state space model and a hybrid model combining Taylor and Fourier methods.
result The hybrid model can predict ODE solutions more accurately, especially for periodic functions.
SurvLatent ODE predicts VTE risk for cancer patients, outperforming current methods.
problem Predicting clinical outcomes from irregularly sampled EHR data with competing events.
method Neural ODE-based Recurrent Neural Networks (ODE-RNN) for flexible survival time estimation.
result SurvLatent ODE outperforms Khorana Risk scores for VTE risk prediction.
In this work we extend the ODE Maximum principle of Hamilton to non-compact hypersurfaces using the Omari-Yau maximum principle at infinity. As an application of this result, we investigate Inverse Mean Curvature Flow (IMCF) of non-compact hypersurfaces in hyperbolic space. Specifically, we look at bounded graphs over …