arXiv subjects

Anirban Samaddar

Publications and source records attributed to Anirban Samaddar.

7 recordsLinked to original sources

arXiv2026

Composing Flow-Matching Energies with Known Physics: Generation, OOD Detection, and Inversion on PDE Fields

Probabilistic modeling of physical fields benefits from both a data-driven prior and known physical structure such as the governing equations. Energy-based models (EBMs) are a natural fit since energies compose additively, which enables augmenting physics information during inference. However, EBMs have been difficult to train and sample from due to the intractable partition function. We show in this work that flow matching models with a potential-induced velocity yield an explicit scalar energy at all transport times, whose gradient is exactly the converted learned score and which recovers the marginal negative log-density at the population optimum. The time-dependent energy functions are obtained purely from the matching regression objective on an independent linear Gaussian interpolation, without a variational form or additional MCMC steps, and the sampling retains the flow ODE. Access to the energy function from a trained model serves three roles: energy-corrected data generation, energy as a scoring function for out-of-distribution (OOD) detection, and energy compositional posterior sampling for inverse problems. In particular, we show the explicit energy permits general MCMC samplers in the predictor-corrector sampling framework, reducing PDE residual and spectral distance compared to the flow ODE baseline. Furthermore, we demonstrate utilizing the data energy and physics-based energy (e.g., PDE residuals) as complementary mechanisms to improve detection accuracy for OOD tasks. In addition, we explore the connection to MCMC-based inference for inverse problems by composing the energy with a quadratic observational likelihood that yields a posterior energy, used as an explicitly chosen family of inference-time targets.

cs.LG↗

arXiv2026

Uncovering Physical Drivers of Dark Matter Halo Structures with Auxiliary-Variable-Guided Generative Models

Deep generative models (DGMs) compress high-dimensional data but often entangle distinct physical factors in their latent spaces. We present an auxiliary-variable-guided framework for disentangling representations of thermal Sunyaev-Zel'dovich (tSZ) maps of dark matter halos. We introduce halo mass and concentration as auxiliary variables and apply a lightweight alignment penalty to encourage latent dimensions to reflect these physical quantities. To generate sharp and realistic samples, we extend latent conditional flow matching (LCFM), a state-of-the-art generative model, to enforce disentanglement in the latent space. Our Disentangled Latent-CFM (DL-CFM) model recovers the established mass-concentration scaling relation and identifies latent space outliers that may correspond to unusual halo formation histories. By linking latent coordinates to interpretable astrophysical properties, our method transforms the latent space into a diagnostic tool for cosmological structure. This work demonstrates that auxiliary guidance preserves generative flexibility while yielding physically meaningful, disentangled embeddings, providing a generalizable pathway for uncovering independent factors in complex astronomical datasets.

stat.ML↗

arXiv2026

Multi-task Modeling for Engineering Applications with Sparse Data

Modern engineering and scientific workflows often require simultaneous predictions across related tasks and fidelity levels, where high-fidelity data is scarce and expensive, while low-fidelity data is more abundant. This paper introduces an Multi-Task Gaussian Processes (MTGP) framework tailored for engineering systems characterized by multi-source, multi-fidelity data, addressing challenges of data sparsity and varying task correlations. The proposed framework leverages inter-task relationships across outputs and fidelity levels to improve predictive performance and reduce computational costs. The framework is validated across three representative scenarios: Forrester function benchmark, 3D ellipsoidal void modeling, and friction-stir welding. By quantifying and leveraging inter-task relationships, the proposed MTGP framework offers a robust and scalable solution for predictive modeling in domains with significant computational and experimental costs, supporting informed decision-making and efficient resource utilization.

stat.ML↗

arXiv2025

Chance-constrained Flow Matching for High-Fidelity Constraint-aware Generation

Generative models excel at synthesizing high-fidelity samples from complex data distributions, but they often violate hard constraints arising from physical laws or task specifications. A common remedy is to project intermediate samples onto the feasible set; however, repeated projection can distort the learned distribution and induce a mismatch with the data manifold. Thus, recent multi-stage procedures attempt to defer projection to clean samples during sampling, but they increase algorithmic complexity and accumulate errors across steps. This paper addresses these challenges by proposing a novel training-free method, Chance-constrained Flow Matching (CCFM), that integrates stochastic optimization into the sampling process, enabling effective enforcement of hard constraints while maintaining high-fidelity sample generation. Importantly, CCFM guarantees feasibility in the same manner as conventional repeated projection, yet, despite operating directly on noisy intermediate samples, it is theoretically equivalent to projecting onto the feasible set defined by clean samples. This yields a sampler that mitigates distributional distortion. Empirical experiments show that CCFM outperforms current state-of-the-art constrained generative models in modeling complex physical systems governed by partial differential equations and molecular docking problems, delivering higher feasibility and fidelity.

cs.LG↗

arXiv2025

Efficient Flow Matching using Latent Variables

Flow matching models have shown great potential in image generation tasks among probabilistic generative models. However, most flow matching models in the literature do not explicitly utilize the underlying clustering structure in the target data when learning the flow from a simple source distribution like the standard Gaussian. This leads to inefficient learning, especially for many high-dimensional real-world datasets, which often reside in a low-dimensional manifold. To this end, we present $\texttt{Latent-CFM}$, which provides efficient training strategies by conditioning on the features extracted from data using pretrained deep latent variable models. Through experiments on synthetic data from multi-modal distributions and widely used image benchmark datasets, we show that $\texttt{Latent-CFM}$ exhibits improved generation quality with significantly less training and computation than state-of-the-art flow matching models by adopting pretrained lightweight latent variable models. Beyond natural images, we consider generative modeling of spatial fields stemming from physical processes. Using a 2d Darcy flow dataset, we demonstrate that our approach generates more physically accurate samples than competing approaches. In addition, through latent space analysis, we demonstrate that our approach can be used for conditional image generation conditioned on latent features, which adds interpretability to the generation process.

cs.CV↗

arXiv2024

REMEDI: Corrective Transformations for Improved Neural Entropy Estimation

Information theoretic quantities play a central role in machine learning. The recent surge in the complexity of data and models has increased the demand for accurate estimation of these quantities. However, as the dimension grows the estimation presents significant challenges, with existing methods struggling already in relatively low dimensions. To address this issue, in this work, we introduce $\texttt{REMEDI}$ for efficient and accurate estimation of differential entropy, a fundamental information theoretic quantity. The approach combines the minimization of the cross-entropy for simple, adaptive base models and the estimation of their deviation, in terms of the relative entropy, from the data density. Our approach demonstrates improvement across a broad spectrum of estimation tasks, encompassing entropy estimation on both synthetic and natural data. Further, we extend important theoretical consistency results to a more generalized setting required by our approach. We illustrate how the framework can be naturally extended to information theoretic supervised learning models, with a specific focus on the Information Bottleneck approach. It is demonstrated that the method delivers better accuracy compared to the existing methods in Information Bottleneck. In addition, we explore a natural connection between $\texttt{REMEDI}$ and generative modeling using rejection sampling and Langevin dynamics.

stat.ML↗

arXiv2022

Sparsity-Inducing Categorical Prior Improves Robustness of the Information Bottleneck

The information bottleneck framework provides a systematic approach to learning representations that compress nuisance information in the input and extract semantically meaningful information about predictions. However, the choice of a prior distribution that fixes the dimensionality across all the data can restrict the flexibility of this approach for learning robust representations. We present a novel sparsity-inducing spike-slab categorical prior that uses sparsity as a mechanism to provide the flexibility that allows each data point to learn its own dimension distribution. In addition, it provides a mechanism for learning a joint distribution of the latent variable and the sparsity and hence can account for the complete uncertainty in the latent space. Through a series of experiments using in-distribution and out-of-distribution learning scenarios on the MNIST, CIFAR-10, and ImageNet data, we show that the proposed approach improves accuracy and robustness compared to traditional fixed-dimensional priors, as well as other sparsity induction mechanisms for latent variable models proposed in the literature.

stat.ML↗