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Flow matching

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

79papers this week−52.4% vs last week

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arXiv math.NAOct 12
A Method for Exact Enforcement of Boundary Conditions on General Curved Triangular Domains: Algorithm and Application to Scientific Machine Learning
Suchuan Dong, Yuchuan Zhang
We present a method for enforcing exactly Dirichlet, Neumann, and Robin conditions on general triangular domains with arbitrarily curved boundaries. The algorithmic constructions developed here complements those in a previous work for general quadrilateral domains. Our method combines (i) the exact mapping between a general curved triangular domain and the standard triangle, (ii) TFC constrained expressions, and (iii) Barnhill transfinite interpolations, to provide explicit closed-form trial ansatze that mathematically satisfy the imposed boundary conditions exactly. Corner compatibility induced by the boundary conditions is pivotal, and enforcing exactly the imposed boundary conditions hinges on the exact enforcement of the induced compatibility constraints. The corner compatibility associated with the acute vertices of the standard triangle and the coupling between gradient components when the hypotenuse corresponds to a Neumann/Robin boundary pose particular challenges. Two strategies are critical to resolving these issues, by reformulating conditional corner constraints into equivalent unconditional forms and by introducing a separate TFC-style auxiliary edge construction…
PDF arXiv
arXiv stat.MLOct 12
Deeply unrolled alternating projections for phase retrieval
Jiayi Yao, Vasileios Charisopoulos, Rebecca Willett
Deep unrolling methods for inverse problems augment traditional reconstruction algorithms with learned priors to improve their performance. These methods have been developed under the implicit assumption that the geometry of the measurement operator does not change between training and deployment; when this is no longer the case, the quality of obtained reconstructions can degrade significantly. In this paper, we argue that this is not an inherent limitation of the deep unrolling paradigm and can be mitigated by a careful choice of the underlying iterative algorithm. We propose a deep unrolling framework for the phase retrieval problem that augments the alternating projections method with a learned denoising step. Our method obtains high-quality reconstructions without the need for retraining in settings where conventional model-based alternatives struggle, such as when the dynamic range of the measurement operator changes significantly at test time.
PDF arXiv
arXiv cs.LGOct 12
Compute-optimal data scaling for neural surrogates via multi-fidelity training
Paul Setinek, Fabian Paischer, Nils Thuerey, Johannes Brandstetter, Felix Koehler
Neural surrogates for Partial Differential Equations (PDEs) are usually trained on synthetic data from numerical simulators. As models grow and scaling laws demand larger datasets, the cost of data generation often outweighs the training cost and becomes the bottleneck in the scaling quest. Unlike data in other domains, however, each PDE sample has a tunable cost that depends on its numerical fidelity, with the resulting cost-accuracy trade-off governed by known convergence rates. We exploit this property by formalizing neural surrogate training as a function of both data quantity and fidelity under a fixed data generation compute budget, treating fidelity as a fine-grained discrete spectrum rather than a binary distinction. Building on this, we show that multi-fidelity training enables Pareto-optimal error scaling against data generation compute. By using simulations at lower fidelities as an additional training signal, training on the optimal fidelity mixture matches the accuracy of high-fidelity-only training, with up to $6.3\times$ less data generation compute across our settings. We validate these findings across six PDE problems spanning structured grids and unstructured…
PDF arXiv
arXiv stat.MEOct 12
Implicit and explicit reparameterizations of the Folded Normal and Rice distributions
Luis Aldama, Kevin Dalton, Minhuan Li, Doeke Hekstra
Variational inference is a flexible tool for modeling experimental data and has proven useful in crystallography. Pathwise gradient estimators provide low-variance gradients for reparameterized variational inference, but are not readily available for some distributions central to crystallography. This work derives and implements implicit and explicit reparameterized gradient estimators for the folded Normal and Rice distributions in \prog{PyTorch}, and compares their variance analytically and empirically. In each case the implicit estimator achieves lower variance for the location derivative, particularly at small location-to-scale ratios, while the scale-derivative variances are nearly equal. For both distributions, implicit estimator is proved to be the conditional expectation of the explicit estimator given the sampled magnitude, so its variance is never larger. As a practical application, French-Wilson scaling is formulated as a variational inference problem, using the folded Normal and Rice distributions as variational families for centric and acentric reflections, respectively. Both estimators recover the exact posterior to better than $1\%$ on the amplitude, and converge…
PDF arXiv
arXiv cs.LGOct 12
SPLICE: Sparse Physics Library Identification and Compositional Expansion
Lucas Thil, Jesse Read, Guillaume Doquet, Rim Kaddah
Neural operator splitting composes a library of neural operators, one per physical mechanism, into zero-shot simulators of new equations. Existing approaches, however, require these mechanisms and their labels to be specified in advance. We ask whether a pretrained library can instead be adapted and grown from unlabeled trajectories in which multiple mechanisms act simultaneously. We introduce SPLICE, a framework that discovers operators without mechanism labels on mixture data. The contributions of the candidate operators to each trajectory are inferred by solving a convex optimization problem. A calibrated test then assigns each discovered operator the mechanism it implements. Failure cases are also detectable, when the library lacks the required physics or when mechanisms are insufficiently separable. Across one and two dimensional systems, the discovered operators recover mechanisms from unlabeled mixtures and compose into zero-shot simulators of unseen equations; a frozen library can also grow an operator for physics absent from pretraining, without labels and without forgetting. On Navier-Stokes, the discovered operators compose about as accurately as their supervised…
PDF arXiv
arXiv cs.LGOct 12
Mixture of GFlowNets
Omar G. Younis, Joseph D. Viviano, Chirayu Anant Haryan, MD Vasimuddin, Sanchit Misra +1
Generative Flow Networks (GFlowNets) learn a policy that samples compositional objects in proportion to an unnormalized reward $R(x)$. This makes them useful wherever many diverse, high-reward candidates are needed and oracle queries are expensive. In practice, a single GFlowNet often fails to cover all modes of a complex distribution, and the obvious ways to scale compute saturate: larger batches and data-parallel gradient averaging draw every trajectory from one, possibly biased, policy, so extra rollouts rediscover known modes instead of finding new ones. We explore whether this mode-bias problem (mode collapse in the extreme) can be addressed with a population of asynchronously trained policies which divide the state space between them. Mixture of GFlowNets (MoG) replaces the single forward policy with a community of $K$ independent GFlowNets coupled through one jointly trained soft classifier, which assigns each member its own region of the state space through reward shaping. Mixing the members under their learned partition functions provably recovers the target $p(x)\propto R(x)$. MoG exchange (MoGX) also lets the classifier route sampled trajectories: a trajectory the…
PDF arXiv

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All in Research →

arXiv math.NAOct 12
A Method for Exact Enforcement of Boundary Conditions on General Curved Triangular Domains: Algorithm and Application to Scientific Machine Learning
Suchuan Dong, Yuchuan Zhang
We present a method for enforcing exactly Dirichlet, Neumann, and Robin conditions on general triangular domains with arbitrarily curved boundaries. The algorithmic constructions developed here complements those in a previous work for general quadrilateral domains. Our method combines (i) the exact mapping between a general curved triangular domain and the standard triangle, (ii) TFC constrained expressions, and (iii) Barnhill transfinite interpolations, to provide explicit closed-form trial ansatze that mathematically satisfy the imposed boundary conditions exactly. Corner compatibility induced by the boundary conditions is pivotal, and enforcing exactly the imposed boundary conditions hinges on the exact enforcement of the induced compatibility constraints. The corner compatibility associated with the acute vertices of the standard triangle and the coupling between gradient components when the hypotenuse corresponds to a Neumann/Robin boundary pose particular challenges. Two strategies are critical to resolving these issues, by reformulating conditional corner constraints into equivalent unconditional forms and by introducing a separate TFC-style auxiliary edge construction…
PDF arXiv
arXiv stat.MLOct 12
Deeply unrolled alternating projections for phase retrieval
Jiayi Yao, Vasileios Charisopoulos, Rebecca Willett
Deep unrolling methods for inverse problems augment traditional reconstruction algorithms with learned priors to improve their performance. These methods have been developed under the implicit assumption that the geometry of the measurement operator does not change between training and deployment; when this is no longer the case, the quality of obtained reconstructions can degrade significantly. In this paper, we argue that this is not an inherent limitation of the deep unrolling paradigm and can be mitigated by a careful choice of the underlying iterative algorithm. We propose a deep unrolling framework for the phase retrieval problem that augments the alternating projections method with a learned denoising step. Our method obtains high-quality reconstructions without the need for retraining in settings where conventional model-based alternatives struggle, such as when the dynamic range of the measurement operator changes significantly at test time.
PDF arXiv
arXiv cs.LGOct 12
Compute-optimal data scaling for neural surrogates via multi-fidelity training
Paul Setinek, Fabian Paischer, Nils Thuerey, Johannes Brandstetter, Felix Koehler
Neural surrogates for Partial Differential Equations (PDEs) are usually trained on synthetic data from numerical simulators. As models grow and scaling laws demand larger datasets, the cost of data generation often outweighs the training cost and becomes the bottleneck in the scaling quest. Unlike data in other domains, however, each PDE sample has a tunable cost that depends on its numerical fidelity, with the resulting cost-accuracy trade-off governed by known convergence rates. We exploit this property by formalizing neural surrogate training as a function of both data quantity and fidelity under a fixed data generation compute budget, treating fidelity as a fine-grained discrete spectrum rather than a binary distinction. Building on this, we show that multi-fidelity training enables Pareto-optimal error scaling against data generation compute. By using simulations at lower fidelities as an additional training signal, training on the optimal fidelity mixture matches the accuracy of high-fidelity-only training, with up to $6.3\times$ less data generation compute across our settings. We validate these findings across six PDE problems spanning structured grids and unstructured…
PDF arXiv
arXiv stat.MEOct 12
Implicit and explicit reparameterizations of the Folded Normal and Rice distributions
Luis Aldama, Kevin Dalton, Minhuan Li, Doeke Hekstra
Variational inference is a flexible tool for modeling experimental data and has proven useful in crystallography. Pathwise gradient estimators provide low-variance gradients for reparameterized variational inference, but are not readily available for some distributions central to crystallography. This work derives and implements implicit and explicit reparameterized gradient estimators for the folded Normal and Rice distributions in \prog{PyTorch}, and compares their variance analytically and empirically. In each case the implicit estimator achieves lower variance for the location derivative, particularly at small location-to-scale ratios, while the scale-derivative variances are nearly equal. For both distributions, implicit estimator is proved to be the conditional expectation of the explicit estimator given the sampled magnitude, so its variance is never larger. As a practical application, French-Wilson scaling is formulated as a variational inference problem, using the folded Normal and Rice distributions as variational families for centric and acentric reflections, respectively. Both estimators recover the exact posterior to better than $1\%$ on the amplitude, and converge…
PDF arXiv
arXiv cs.LGOct 12
SPLICE: Sparse Physics Library Identification and Compositional Expansion
Lucas Thil, Jesse Read, Guillaume Doquet, Rim Kaddah
Neural operator splitting composes a library of neural operators, one per physical mechanism, into zero-shot simulators of new equations. Existing approaches, however, require these mechanisms and their labels to be specified in advance. We ask whether a pretrained library can instead be adapted and grown from unlabeled trajectories in which multiple mechanisms act simultaneously. We introduce SPLICE, a framework that discovers operators without mechanism labels on mixture data. The contributions of the candidate operators to each trajectory are inferred by solving a convex optimization problem. A calibrated test then assigns each discovered operator the mechanism it implements. Failure cases are also detectable, when the library lacks the required physics or when mechanisms are insufficiently separable. Across one and two dimensional systems, the discovered operators recover mechanisms from unlabeled mixtures and compose into zero-shot simulators of unseen equations; a frozen library can also grow an operator for physics absent from pretraining, without labels and without forgetting. On Navier-Stokes, the discovered operators compose about as accurately as their supervised…
PDF arXiv
arXiv cs.LGOct 12
Mixture of GFlowNets
Omar G. Younis, Joseph D. Viviano, Chirayu Anant Haryan, MD Vasimuddin, Sanchit Misra +1
Generative Flow Networks (GFlowNets) learn a policy that samples compositional objects in proportion to an unnormalized reward $R(x)$. This makes them useful wherever many diverse, high-reward candidates are needed and oracle queries are expensive. In practice, a single GFlowNet often fails to cover all modes of a complex distribution, and the obvious ways to scale compute saturate: larger batches and data-parallel gradient averaging draw every trajectory from one, possibly biased, policy, so extra rollouts rediscover known modes instead of finding new ones. We explore whether this mode-bias problem (mode collapse in the extreme) can be addressed with a population of asynchronously trained policies which divide the state space between them. Mixture of GFlowNets (MoG) replaces the single forward policy with a community of $K$ independent GFlowNets coupled through one jointly trained soft classifier, which assigns each member its own region of the state space through reward shaping. Mixing the members under their learned partition functions provably recovers the target $p(x)\propto R(x)$. MoG exchange (MoGX) also lets the classifier route sampled trajectories: a trajectory the…
PDF arXiv

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Flow matching

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Flow matching

Recent papers

A Method for Exact Enforcement of Boundary Conditions on General Curved Triangular Domains: Algorithm and Application to Scientific Machine Learning

Deeply unrolled alternating projections for phase retrieval

Compute-optimal data scaling for neural surrogates via multi-fidelity training

Implicit and explicit reparameterizations of the Folded Normal and Rice distributions

SPLICE: Sparse Physics Library Identification and Compositional Expansion

Mixture of GFlowNets

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Recent papers

A Method for Exact Enforcement of Boundary Conditions on General Curved Triangular Domains: Algorithm and Application to Scientific Machine Learning

Deeply unrolled alternating projections for phase retrieval

Compute-optimal data scaling for neural surrogates via multi-fidelity training

Implicit and explicit reparameterizations of the Folded Normal and Rice distributions

SPLICE: Sparse Physics Library Identification and Compositional Expansion

Mixture of GFlowNets