Papers

Field

Top tools here

Open problems in Flow matching

Stable and scalable source-target pairing for flow matching1 paper raises it · 1 addresses it
Unstable or random pairing degrades training and integration, limiting model performance at scale.
- Scaling Online Optimal Transport Minibatches for Flow Matchingraises · addresses
Efficient few-step generation without fixed discretization1 paper raises it · 1 addresses it
Fixed timestep discretization in flow matching is heuristic, expensive to tune, and restrictive for varying sample difficulty.
- Few-Step Generation via Data-Space Iterationraises · addresses
Data-free and simulation-free distillation for flow/diffusion models1 paper raises it · 1 addresses it
Existing distillation methods rely on curated datasets, costly teacher rollouts, or auxiliary networks, complicating training and scaling.
- Consistent Distribution Matching for Data-Free Diffusion Distillationraises · addresses
Accelerating numerical integration for neuro-spectral PDE solvers1 paper raises it · 1 addresses it
Sequential time-stepping in neuro-spectral architectures limits temporal parallelism and slows training/inference.
- PaPi: Parallel Picard-Duhamel Integration for Fast Neuro-Spectral Architecturesraises · addresses
Dynamics-aligned latent spaces for PDE representation learning1 paper raises it · 1 addresses it
Reconstruction-based objectives fail to capture evolution geometry, limiting accurate field prediction.
- PDE-JEPA: Predictive Representation Learning of Latent Dynamics Modeling for Parametric PDEsraises · addresses

Named by an AI from these papers' abstracts.

Open problems

Recently funded

Topics in this field

flow matching · flow · generative modeling301 papers33 this week
physics informed neural · neural operators · informed neural networks295 papers27 this week
diffusion priors · posterior sampling · diffusion posterior75 papers16 this week

Topics in this field

Active contributors · 90 days

Anima AnandkumarNeural Operator Splitting for Fluid Dynamics in Complex Geometry5
Stefan T. RadevConditional Mean Flows: Few-Step Densities for Simulation-Based Inference5
Taiji SuzukiFinite-Sample Approximation of Hessian-Guided Perturbed Wasserstein Gradient Flows5
Alexander TongImproved Training of Strong Stochastic Flow Maps4
Jing XuSame Target, Different Origins: Aligning Latent Rollout for Consistent PDE Emulation4
Jun ZhangEqual Path Cost, Unequal Output Effects: Understanding Perturbation Propagation in Diffusion Models4

Active contributors

Activity · 12 weeks

Activity

Recent papers

All papers in Research

arXiv cs.LGSep 24
Beyond Compression: Training Latent Representations for Stable Long-Horizon Rollout in Neural Surrogate Solvers
Andreas E. Robertson, Ashley T. Lenau, John D. Shimanek, Benjamin A. Jasperson, Vivek Oommen +3
Latent neural surrogate solvers, or latent dynamics models, accelerate simulations of time-dependent physical systems by evolving a compressed latent space rather than resolving full-resolution fields directly. In principle this reduces computational cost and simplifies learning, but in practice errors often accumulate rapidly during long autoregressive rollouts, limiting predictive utility. We show that this instability does not stem from the latent representation itself, but arises when it is trained solely for reconstruction, producing representations poorly suited to long-horizon forecasting. We systematically evaluate training-level interventions that align latent representations with long-horizon rollout: Koopman operator learning and Hamming noise injection during autoencoder training to improve compression, together with noise injection and multi-step rollout fine-tuning to improve dynamics. Interventions that improve long-horizon rollout stability often degrade conventional training metrics, including reconstruction and one-step prediction accuracy. Collectively, these interventions reduce long-rollout error by approximately 40\% and match or exceed the accuracy of…
PDF arXiv
arXiv eess.SYSep 24
GridSFM: A Foundation Model for Solving AC Optimal Power Flow
Luke Bhan, Weiwei Yang, Margaret Capetz, Baosen Zhang
We introduce GridSFM, a framework that combines a pretrained foundation model across grid topologies with physics-informed fine-tuning for solving AC Optimal Power Flow (AC-OPF) at scale. It is a $15$ million parameter physics-inspired graph neural network pretrained across $54$ topologies of $500$ to $4{,}000$ buses. Our model attains a $2.45\%$ zero-shot generation-cost error on a $10{,}000$ bus case held-out operating conditions with no degradation as system size grows. Building on this, we pair the pretrained backbone with a physics-informed fine-tuning design based on Newton's method for power flow. With only $100$ solved instances, GridSFM adapts to unseen grids up to $10{,}000$ buses. We show it out performs single topology, dedicated neural network models that are trained more data, both in terms of cost and solver iterations when deployed as warm starting points. In designing this foundation model, we overcome the fact that the feasible set for AC-OPF can be disconnected. This is an obstruction that prevents any continuous neural network from approximating the solution map. To do so, we lift the problem and relax its constraints with logarithmically penalized slacks. We…
PDF arXiv
arXiv cs.NESep 24
Orbital Error Dynamics: Self-Organized Criticality, Ephemeral Parameter Resonance, and Non-Linear Biological Ontologies in Zero-Storage Neural Synthesis
Volkan Dağlı, Zerrin Dağlı, Dağhan Dağlı
Modern deep neural networks treat parameters as static floating-point matrices stored in physical memory, incurring Von Neumann memory bottlenecks and representation collapse. We formulate Orbital Error Dynamics (OED), an analytical framework wherein synaptic weights are not stored masses (O(W)), but transient topological resonances (O(1)) derived procedurally from the complex quadratic polynomial map z_{n+1} = z_n^2 + c. We introduce the Bent Sine Wave Hypothesis, demonstrating that non-equilibrium living systems emerge when harmonic waves curl inward through environmental drag toward the cardioid cusp (c = 1/4). We define the Observer Horizon Geometry in parameter space, identifying interior resonance shoulder loci X_upper = (0.25, +0.18) and X_lower = (0.25, -0.18) between the fixed-point basin and the true boundary at c = 0.25 +/- 0.50i. To escape non-convex stagnation without loss zeroing, we introduce a heavy-tailed Biomimetic Perturbed Jump Operator (Omega_tunneling) inspired by mammalian fertilization zinc sparks. We further couple an enteric-cranial Dual-Brain architecture shielded by adaptive CD4+ regulatory immune gating (M_CD4), and project the 4-nucleotide genetic…
PDF arXiv
arXiv stat.MLSep 24
Nuclear Norm-Regularized Bayesian Matrix Completion
Calvin Tolbert
Matrix completion, the problem of estimating missing entries in a matrix from noisily observed ones, underlies a diverse array of problems such as recommender systems and counterfactual outcome estimation in panel data. Many algorithms address the problem using regularized least squares, often with the nuclear norm as a regularizer, but this method yields a point estimate with no built-in uncertainty quantification. A Bayesian formulation is a natural alternative, and if the noise variance is known, the nuclear norm-based prior yields a log-concave posterior. Unfortunately, in practice, the noise variance will not be known a priori, so for a fully Bayesian approach, a prior must be imposed on it. We give the first sampler for this model with an explicit non-asymptotic guarantee: polynomial in the matrix dimensions and in the reciprocal of the target accuracy. Our technique is to discretize the distribution of the noise precision onto a grid and build a categorical posterior via thermodynamic integration. This extension is not specific to matrix completion and may be useful in other non-log-concave sampling problems where the non-log-concavity is restricted to a single variable…
PDF arXiv
arXiv hep-latSep 24
Accurate Sampling from Diffusion Models
Dénes Sexty
A new proposal called DM-SMC (Diffusion Model - Sequential Monte Carlo) is investigated, which samples ensembles defined in terms of an action, using diffusion models trained on samples from the ensemble. The SMC setup allows for accurate sampling in spite of an approximate diffusion model and the finite stepsize used in the numerical solution of the stochastic process. Improved update strategies are also investigated. Results are presented for a $Z_2$ symmetric scalar field theory in 2 dimensions near its 2nd order phase transition.
PDF arXiv
arXiv math.NASep 24
Elucidating the Conformal Structure of the Brinkman Penalisation Method for Geometry-Adapted, Structure-Preserving Operator Learning of Hamiltonian PDEs
Teo Deveney, Baige Xu, Takaharu Yaguchi
The Brinkman penalisation method embeds boundary-value problems on complex domains into a simple computational box by modeling the solid region as a strongly dissipative medium, avoiding body-fitted mesh generation. We show that multi-symplectic Hamiltonian PDEs regularised by Brinkman-type penalisation retain a multi-conformal symplectic structure under a compatibility condition linking the symplectic matrix and the penalisation projection. This yields an exact local conservation law, under which the multi-symplectic two-form is conserved in the fluid region and decays exponentially inside the solid. The linear wave equation with Brinkman friction and Maxwell's equations with artificial Ohmic conductivity satisfy this condition, with explicit modified Hamiltonian densities. Building on this, we propose (i) structure-preserving numerical integrators via Strang splitting that satisfy a discrete conformal conservation law, and (ii) conformal symplectic neural operators that interleave exact dissipative flows with learnable multi-symplectic evolution operators, allowing geometry-dependent operator learning. Numerical experiments on wave and electromagnetic scattering demonstrate…
PDF arXiv

Papers

Topics in this field

flow matching · flow · generative modeling301 papers33 this week
physics informed neural · neural operators · informed neural networks295 papers27 this week
diffusion priors · posterior sampling · diffusion posterior75 papers16 this week

Active contributors · 90 days

Anima AnandkumarNeural Operator Splitting for Fluid Dynamics in Complex Geometry5
Stefan T. RadevConditional Mean Flows: Few-Step Densities for Simulation-Based Inference5
Taiji SuzukiFinite-Sample Approximation of Hessian-Guided Perturbed Wasserstein Gradient Flows5
Alexander TongImproved Training of Strong Stochastic Flow Maps4
Jing XuSame Target, Different Origins: Aligning Latent Rollout for Consistent PDE Emulation4
Jun ZhangEqual Path Cost, Unequal Output Effects: Understanding Perturbation Propagation in Diffusion Models4

Recent papers

All papers in Research

arXiv cs.LGSep 24
Beyond Compression: Training Latent Representations for Stable Long-Horizon Rollout in Neural Surrogate Solvers
Andreas E. Robertson, Ashley T. Lenau, John D. Shimanek, Benjamin A. Jasperson, Vivek Oommen +3
Latent neural surrogate solvers, or latent dynamics models, accelerate simulations of time-dependent physical systems by evolving a compressed latent space rather than resolving full-resolution fields directly. In principle this reduces computational cost and simplifies learning, but in practice errors often accumulate rapidly during long autoregressive rollouts, limiting predictive utility. We show that this instability does not stem from the latent representation itself, but arises when it is trained solely for reconstruction, producing representations poorly suited to long-horizon forecasting. We systematically evaluate training-level interventions that align latent representations with long-horizon rollout: Koopman operator learning and Hamming noise injection during autoencoder training to improve compression, together with noise injection and multi-step rollout fine-tuning to improve dynamics. Interventions that improve long-horizon rollout stability often degrade conventional training metrics, including reconstruction and one-step prediction accuracy. Collectively, these interventions reduce long-rollout error by approximately 40\% and match or exceed the accuracy of…
PDF arXiv
arXiv eess.SYSep 24
GridSFM: A Foundation Model for Solving AC Optimal Power Flow
Luke Bhan, Weiwei Yang, Margaret Capetz, Baosen Zhang
We introduce GridSFM, a framework that combines a pretrained foundation model across grid topologies with physics-informed fine-tuning for solving AC Optimal Power Flow (AC-OPF) at scale. It is a $15$ million parameter physics-inspired graph neural network pretrained across $54$ topologies of $500$ to $4{,}000$ buses. Our model attains a $2.45\%$ zero-shot generation-cost error on a $10{,}000$ bus case held-out operating conditions with no degradation as system size grows. Building on this, we pair the pretrained backbone with a physics-informed fine-tuning design based on Newton's method for power flow. With only $100$ solved instances, GridSFM adapts to unseen grids up to $10{,}000$ buses. We show it out performs single topology, dedicated neural network models that are trained more data, both in terms of cost and solver iterations when deployed as warm starting points. In designing this foundation model, we overcome the fact that the feasible set for AC-OPF can be disconnected. This is an obstruction that prevents any continuous neural network from approximating the solution map. To do so, we lift the problem and relax its constraints with logarithmically penalized slacks. We…
PDF arXiv
arXiv cs.NESep 24
Orbital Error Dynamics: Self-Organized Criticality, Ephemeral Parameter Resonance, and Non-Linear Biological Ontologies in Zero-Storage Neural Synthesis
Volkan Dağlı, Zerrin Dağlı, Dağhan Dağlı
Modern deep neural networks treat parameters as static floating-point matrices stored in physical memory, incurring Von Neumann memory bottlenecks and representation collapse. We formulate Orbital Error Dynamics (OED), an analytical framework wherein synaptic weights are not stored masses (O(W)), but transient topological resonances (O(1)) derived procedurally from the complex quadratic polynomial map z_{n+1} = z_n^2 + c. We introduce the Bent Sine Wave Hypothesis, demonstrating that non-equilibrium living systems emerge when harmonic waves curl inward through environmental drag toward the cardioid cusp (c = 1/4). We define the Observer Horizon Geometry in parameter space, identifying interior resonance shoulder loci X_upper = (0.25, +0.18) and X_lower = (0.25, -0.18) between the fixed-point basin and the true boundary at c = 0.25 +/- 0.50i. To escape non-convex stagnation without loss zeroing, we introduce a heavy-tailed Biomimetic Perturbed Jump Operator (Omega_tunneling) inspired by mammalian fertilization zinc sparks. We further couple an enteric-cranial Dual-Brain architecture shielded by adaptive CD4+ regulatory immune gating (M_CD4), and project the 4-nucleotide genetic…
PDF arXiv
arXiv stat.MLSep 24
Nuclear Norm-Regularized Bayesian Matrix Completion
Calvin Tolbert
Matrix completion, the problem of estimating missing entries in a matrix from noisily observed ones, underlies a diverse array of problems such as recommender systems and counterfactual outcome estimation in panel data. Many algorithms address the problem using regularized least squares, often with the nuclear norm as a regularizer, but this method yields a point estimate with no built-in uncertainty quantification. A Bayesian formulation is a natural alternative, and if the noise variance is known, the nuclear norm-based prior yields a log-concave posterior. Unfortunately, in practice, the noise variance will not be known a priori, so for a fully Bayesian approach, a prior must be imposed on it. We give the first sampler for this model with an explicit non-asymptotic guarantee: polynomial in the matrix dimensions and in the reciprocal of the target accuracy. Our technique is to discretize the distribution of the noise precision onto a grid and build a categorical posterior via thermodynamic integration. This extension is not specific to matrix completion and may be useful in other non-log-concave sampling problems where the non-log-concavity is restricted to a single variable…
PDF arXiv
arXiv hep-latSep 24
Accurate Sampling from Diffusion Models
Dénes Sexty
A new proposal called DM-SMC (Diffusion Model - Sequential Monte Carlo) is investigated, which samples ensembles defined in terms of an action, using diffusion models trained on samples from the ensemble. The SMC setup allows for accurate sampling in spite of an approximate diffusion model and the finite stepsize used in the numerical solution of the stochastic process. Improved update strategies are also investigated. Results are presented for a $Z_2$ symmetric scalar field theory in 2 dimensions near its 2nd order phase transition.
PDF arXiv
arXiv math.NASep 24
Elucidating the Conformal Structure of the Brinkman Penalisation Method for Geometry-Adapted, Structure-Preserving Operator Learning of Hamiltonian PDEs
Teo Deveney, Baige Xu, Takaharu Yaguchi
The Brinkman penalisation method embeds boundary-value problems on complex domains into a simple computational box by modeling the solid region as a strongly dissipative medium, avoiding body-fitted mesh generation. We show that multi-symplectic Hamiltonian PDEs regularised by Brinkman-type penalisation retain a multi-conformal symplectic structure under a compatibility condition linking the symplectic matrix and the penalisation projection. This yields an exact local conservation law, under which the multi-symplectic two-form is conserved in the fluid region and decays exponentially inside the solid. The linear wave equation with Brinkman friction and Maxwell's equations with artificial Ohmic conductivity satisfy this condition, with explicit modified Hamiltonian densities. Building on this, we propose (i) structure-preserving numerical integrators via Strang splitting that satisfy a discrete conformal conservation law, and (ii) conformal symplectic neural operators that interleave exact dissipative flows with learnable multi-symplectic evolution operators, allowing geometry-dependent operator learning. Numerical experiments on wave and electromagnetic scattering demonstrate…
PDF arXiv

Activity · 12 weeks

Open problems in Flow matching

Stable and scalable source-target pairing for flow matching1 paper raises it · 1 addresses it
Unstable or random pairing degrades training and integration, limiting model performance at scale.
- Scaling Online Optimal Transport Minibatches for Flow Matchingraises · addresses
Efficient few-step generation without fixed discretization1 paper raises it · 1 addresses it
Fixed timestep discretization in flow matching is heuristic, expensive to tune, and restrictive for varying sample difficulty.
- Few-Step Generation via Data-Space Iterationraises · addresses
Data-free and simulation-free distillation for flow/diffusion models1 paper raises it · 1 addresses it
Existing distillation methods rely on curated datasets, costly teacher rollouts, or auxiliary networks, complicating training and scaling.
- Consistent Distribution Matching for Data-Free Diffusion Distillationraises · addresses
Accelerating numerical integration for neuro-spectral PDE solvers1 paper raises it · 1 addresses it
Sequential time-stepping in neuro-spectral architectures limits temporal parallelism and slows training/inference.
- PaPi: Parallel Picard-Duhamel Integration for Fast Neuro-Spectral Architecturesraises · addresses
Dynamics-aligned latent spaces for PDE representation learning1 paper raises it · 1 addresses it
Reconstruction-based objectives fail to capture evolution geometry, limiting accurate field prediction.
- PDE-JEPA: Predictive Representation Learning of Latent Dynamics Modeling for Parametric PDEsraises · addresses

Named by an AI from these papers' abstracts.

Fields · AI · updated 17m ago

Flow matching

Found by the topic model: flow matching, physics informed neural, diffusion priors.

76papers this week−51.0% vs last week

All papers · 671 With code · 3

Newest Most relevant

632 papers this month