Refined Grid Sampling for Efficient Implicit Neural Representations of Large-Scale Scientific Data

Implicit Neural Representations (INRs) have emerged as promising surrogates for large 3D scientific simulations due to their ability to continuously model spatial and conditional fields, yet they face a critical fidelity-speed dilemma: deep MLPs suffer from high inference cost, while efficient embedding-based models lack sufficient expressiveness. To resolve this, we propose the Decoupled Representation Refinement (DRR) architectural paradigm. DRR leverages a deep refiner network, alongside non-parametric transformations, in a one-time offline process to encode rich representations into a compact and efficient embedding structure. This approach decouples slow neural networks with high representational capacity from the fast inference path. We introduce DRR-Net, a simple network that validates this paradigm, and a novel data augmentation strategy, Variational Pairs (VP) for improving INRs under complex tasks like high-dimensional surrogate modeling. Experiments on several ensemble simulation datasets demonstrate that our approach achieves state-of-the-art fidelity, while being up to 27$\times$ faster at inference than high-fidelity baselines and remaining competitive with the fastest models. The DRR paradigm offers an effective strategy for building powerful and practical neural field surrogates and INRs in broader applications, with a minimal compromise between speed and quality.

Implicit neural representations (INRs) provide a flexible framework for modeling high-dimensional continuous fields, but their training is often inefficient due to uniform subsampling that ignores spatial heterogeneity. Existing adaptive sampling methods partially address this issue by prioritizing high-error samples, but typically operate at the point level, often leading to redundant sampling in localized regions and insufficient coverage of the domain. We propose ACES (Adaptive Coverage-aware Efficient Sampling), a structured sampling framework that improves training efficiency by decoupling coverage and importance. ACES constructs adaptive spatial partitions to ensure domain coverage and reduce redundancy, and applies region-level importance weighting to prioritize informative regions during training. We provide a theoretical analysis showing that adaptive partitioning reduces gradient variance by increasing within-region homogeneity, and that controlled bias in region-level weighting may improve optimization efficiency relative to standard unbiased estimators. Experiments on scientific field learning tasks demonstrate that ACES achieves faster convergence and lower error than uniform and pointwise adaptive sampling baselines, with the largest gains in fields with highly localized complexity.

Implicit neural representations (INRs) for time-varying volumetric data are typically trained using dense sampling over spatiotemporal coordinates, where each observation corresponds to a single point in space and time. This coordinate-wise formulation requires extensive sampling during optimization, leading to high computational cost and inefficient use of temporal structure. In this work, we revisit this design choice and show that dense spatiotemporal sampling is not necessary for learning time-varying fields. Instead, we represent the data as a collection of spatially indexed time series and train INRs using sequence-level supervision over each spatial location, rather than coordinate-wise scalar samples. This reformulation eliminates the need for dense spatiotemporal sampling and instead learns each spatial location from its full temporal evolution in a structured manner. We demonstrate that this representation is compatible with a range of existing INR architectures and consistently improves reconstruction quality, while significantly reducing training cost. Furthermore, we show that this formulation can be combined with mixture-of-experts architectures, and that our MoE instantiation further improves reconstruction quality compared to both the base reformulation and existing MoE-based INR methods, providing a stronger capacity allocation under heterogeneous temporal dynamics.