# FA-INR: Adaptive Implicit Neural Representations for Interpretable Exploration of Simulation Ensembles

arXiv: https://arxiv.org/abs/2506.06858 · HTML: https://mlsanity.com/paper/2506.06858/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Vision mixture-of-experts, one of 12 directions in Mixture-of-experts.
- Builds on 50 of its 65 references that are in the map.
- First posted on arXiv 7 Jun 2025.

## Placed in

- Mixture-of-experts / [Vision mixture-of-experts](https://mlsanity.com/moe/vision-mixture-of-experts/)

## Builds on (most cited first, 30 of 50)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Scaling Vision with Sparse Mixture of Experts](https://mlsanity.com/paper/2106.05974/) (2021)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [Learned Initializations for Optimizing Coordinate-Based Neural Representations](https://mlsanity.com/paper/2012.02189/) (2020)
- [Memorizing Transformers](https://mlsanity.com/paper/2203.08913/) (2022)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [DeRF: Decomposed Radiance Fields](https://mlsanity.com/paper/2011.12490/) (2020)
- [A Review of Sparse Expert Models in Deep Learning](https://mlsanity.com/paper/2209.01667/) (2022)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning](https://mlsanity.com/paper/2412.00568/) (2024)
- [Large Memory Layers with Product Keys](https://mlsanity.com/paper/1907.05242/) (2019)
- [DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting](https://mlsanity.com/paper/2306.01984/) (2023)
- [Operator Learning with Neural Fields: Tackling PDEs on General Geometries](https://mlsanity.com/paper/2306.07266/) (2023)
- [Continuous PDE Dynamics Forecasting with Implicit Neural Representations](https://mlsanity.com/paper/2209.14855/) (2022)
- [Dynamic CT Reconstruction from Limited Views with Implicit Neural Representations and Parametric Motion Fields](https://mlsanity.com/paper/2104.11745/) (2021)
- [Geometry Aware Operator Transformer as an Efficient and Accurate Neural Surrogate for PDEs on Arbitrary Domains](https://mlsanity.com/paper/2505.18781/) (2025)

## Built on by (most cited first, 1 of 1)

- [Refine Now, Query Fast: A Decoupled Refinement Paradigm for Implicit Neural Fields](https://mlsanity.com/paper/2602.15155/) (2026)

## Abstract (arXiv)

Surrogate models are essential for efficient exploration of large-scale ensemble simulations. Implicit neural representations (INRs) provide a compact and continuous framework for modeling spatially structured data, but they often struggle with learning complex localized structures within the scientific fields. Recent INR-based surrogates address this by augmenting INRs with explicit feature structures, but at the cost of flexibility and substantial memory overhead. In this paper, we present Feature-Adaptive INR (FA-INR), an adaptive INR-based surrogate model for high-fidelity and interpretable exploration of ensemble simulations. Instead of relying on structured feature representations, FA-INR leverages cross-attention over a learnable key-value memory bank to allocate model capacity adaptively based on the data characteristics. To further improve scalability, we introduce a coordinate-guided mixture of experts (MoE) framework that enhances both efficiency and specialization of feature representations. More importantly, the learned experts produce an interpretable partition over the simulation domain, enabling scientists to identify complex structures and perform localized parameter-space exploration. Beyond quantitative and qualitative evaluations, we also demonstrate that our learned expert specialization can reveal meaningful scientific insights and support localized sensitivity analysis.