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Neural fields in the geosciences, 2025–2026

Report 18 · Compression, reconstruction and physics constraints across ocean, atmosphere, land and ice

Abstract

Neural fields now clearly win for gridless reconstruction from sparse, irregular observations (altimeter tracks, stations, CryoSat-2 point clouds, seismic and gravity inversion), and as differentiable state parameterizations for variational assimilation, where the network’s spectral bias stands in for a background covariance. However, for the archival compression of reanalysis they still lose to tuned error-bounded codecs, and a 2026 ERA5 head-to-head found that SZ3.1 leads at every error bound. Atmospheric-composition fields (methane, NO₂, XCO₂) have essentially no neural-field work. What GeoStack should do about it is on the neural-fields design page.

Keywords:neural fieldsimplicit neural representationsSIRENcompressioninterpolationdata assimilationphysics-informed

Key findings

  1. Spherical handling has converged on a few recipes. Spherical-harmonic embeddings into a SIREN Rußwurm et al., 2024 are the baseline. However, work in 2025 showed that they fail on small or fragmented regions such as islands and coasts, and it proposed spherical wavelet encodings instead Cai & Balestriero, 2025. HEALPix hybrid grids and learnable spherical Voronoi partitions are the alternatives.

  2. Compression claims need careful reading. Most INR compression papers compare against JPEG2000 or against vanilla INRs, and not against SZ3/ZFP at matched error bounds. When the comparison is done properly, SZ3 is hard to beat on smooth gridded fields.

  3. Gridless reconstruction is the killer application. Neural fields consume point clouds without regridding, and they give analytic derivatives for geostrophy, elevation-change rates and PDE residuals.

  4. Spectral bias is being reframed as a feature. In 4D-Var and in geophysical inversion, the MLP’s preference for low frequencies acts as an implicit regularizer, which replaces the hand-built background covariances or smoothness penalties.

  5. Amortization across samples is thin in practice. Functa, CORAL and DINo-style modulations are mature on ML benchmarks, whereas the real geoscience deployments are few (PINROD for the ocean, and the multi-altitude climate INRs).

  6. JAX code exists but is scattered. There is BayesNF (Google), DIFFICE-jax (ice shelves), PINNICLE through DeepXDE’s JAX backend, and DeepMind’s functa. However, no sphere-aware, geoscience-specific neural-field library exists in JAX.

Compression and storage reduction

Neural fields do not dominate archival compression in 2026. Their advantages are random-access continuous queries, analytic gradients, context conditioning and compression as an embedding.

WorkGroup, venueField representsArchitecture and encodingKey resultCode
Compressing weather and climate data into neural networks (foundation) Huang & Hoefler, 2023Huang & Hoefler (ETH), ICLR 2023(lat, lon, level, time) → ERA5 variableCoordinate MLP, Fourier features, quantized weights300× to 3,000×; beats SZ3 on weighted RMSE/MAE; 790× WeatherBench loader with < 2% RMSE risePyTorch
HiHa Xu & others, 2025Xu et al. (Jilin), Computers & Geosciences 2025Spherical coords + level → atmospheric variables3-D FFT band split; multi-scale INR for low, octree-local SIRENs for mid, sparse storage for high frequenciesTargets 204 variables on 37 levels; explicit fix for spectral biasnot confirmed
CA-INR Mostajeran et al., 2025Mostajeran et al. (Utah), Scientific Reports 2025(space, time, context) → E3SM surface temperatureMLP with topography and climatology as context inputsRatio 140 on benchmarks; 500 years of CESM at 200; context adds up to 11.46 dB PSNRnot confirmed
Multi-altitude climate INRs Abdul Qayyum et al., 2024Abdul Qayyum et al. (BNL / TAMU), MLSP 2024; NeurIPS 2025 CCAILow-res latent + coordinate → multi-altitude windEncoders + EDSR features + LIIF coordinate decoderCompression, arbitrary-scale reconstruction and modality fusion in one modelnot confirmed
Hybrid Neural Representations for Spherical Data Hybrid Neural Representations for Spherical Data, 2024ICML 2024, arXiv 2402.05965Sphere → ERA5 / CMBHEALPix grid features + MLP decoderStrong sphere-native baseline—
Climplicit Dollinger et al., 2025Dollinger et al. (EcoVision UZH), arXiv 2504.05089(lon, lat, month) → CHELSA climatology embeddingResidual SIREN blocks16 MB model replaces 99.97% of CHELSA; ×3,500 less diskGitHub
ImplicitTerrainV2 ImplicitTerrainV2, 2026arXiv 2026(x, y) → elevationWavelet-guided adaptive SIREN + quantization + entropy codingBeats ZSTD, ZFP, LERC at 0.5–2 bpp; SZ3 still wins (80.45 dB at 1.96 bpp vs 65.97 dB at 1.23 bpp)—
Can DNNs improve compression of very large scientific data? Can Deep Neural Networks Improve Compression of Very Large Scientific Data?, 2026arXiv 2026ERA5 via learned predictorsCRA5, GraphCast, Aurora as predictors vs SZ3.1, same backendNo learned predictor improves dataset-level compression; up to 9.6× per-variable gains—

For context outside INRs, DeepMind’s Neural Compression of Atmospheric States Mirowski & others, 2024 uses HEALPix with hyperprior and vector-quantized autoencoders to reach more than 1,000× at about one second per global state, which is the bar that INRs must beat. The 2025 review Lossy Neural Compression for Geospatial Analytics Gomes & others, 2025 calls the compression efforts for Earth-system models limited, and it says that the shortcomings of INRs must be fixed first.

So one should benchmark against SZ3/ZFP at a matched maximum error, and not just on PSNR.

Interpolation, gap-filling and continuous reconstruction

This is where neural fields are strongest, as point clouds and swaths go in and a continuous, differentiable field comes out.

Ocean

Atmosphere and near-surface weather

Land and solid Earth

Ice and cryosphere

Location encoders

Physics-constrained neural fields

The live frontier is in three places: 1) neural-field 4D-Var, 2) PINN inversion for the ice and the ocean, and 3) latent dynamics over INR codes.

WorkVenueNeural-field rolePhysicsResultCode
Neural field reparameterization for 4DVARJaemin Oh, arXiv 2025 (v2 2026) Oh, 2025Full state x(s,t)∈Rx(\vect{s}, t) \in \mathbb{R} as one field4D-Var cost + physics losses, parallel-in-timeBetter initial conditions than classical 4D-Var on 2-D Kolmogorov and 3-D Taylor–Green; spectral bias replaces an explicit background covariance Σx\gmat{\Sigma}_x; separable PINNs give large speedups; no ground-truth training data—
StrAss-PINN: deep learning in the abyssarXiv 2025 StrAss-PINN: Deep learning in the abyss, 2025SIREN-style field per ocean layer3-layer quasi-geostrophicDeep flow from SWOT-like SSH, ARGO-like interior, sparse deep-ARGO—
PINRODZhao, Luo et al. (BNL/LANL/ANL), ICLR 2025 CCAI Zhao et al., 2025DINo-style INR decoder + latent codesParameterized latent neural ODEResolution-independent baroclinic ocean surrogate—
Deep learning the flow law of Antarctic ice shelvesWang et al., Science 2025 Wang et al., 2025MLPs for velocity, thickness, viscosityShallow-shelf approximationGrain-size-sensitive rheology in compression zones; anisotropic viscosity at suture zonesDIFFICE-jax (JAX)
PINNICLE v1.0Cheng, Krishna, Morlighem, GMD 2025 Cheng et al., 2025(x, y) → ice fieldsSSA, MOLHO, mass conservation; forward and inverseGeneral ice-sheet PINN libraryGitHub
Subglacial topography from two conservation lawsKrishna, Cheng, Morlighem, The Cryosphere 2026 Krishna et al., 2026PINN for thickness + basal shearMass conservation + SSASingle-law PINNs insufficient in sparse regions; finds bed features absent from BedMachinePINNICLE
PINN surface currents from driftersFrontiers in Marine Science 2025(x, y, t) → velocityFlow equations as soft constraintsPhysics term essential for Eulerian fields from Lagrangian drifters—

The latent-dynamics foundations are DINo Yin & others, 2023, which pairs an INR decoder with a latent ODE, CORAL Serrano & others, 2023, which uses shift-modulated SIRENs with meta-learned codes for operator learning on irregular grids, and AROMA Serrano & others, 2024, which uses local neural fields with transformer latent dynamics and beats both on harder systems.

ProblemWhere the field isOpen gap
Sphere and geodesic coordinatesSH(λ, φ) → SIREN is standard; spherical wavelets, HEALPix hybrid grids, spherical Voronoi emergingSH cost grows as L² and underserves small landmasses; no native multiresolution hash grid on the sphere
Multiscale and spectral biasExplicit band split (HiHa), wavelet-guided local nets (ImplicitTerrainV2), spectral bias as regularizer (neural 4D-Var, inversion)Fidelity tasks fight spectral bias; ill-posed inverse problems exploit it
ScalabilitySeparable nets (SPINN), hash grids (IntraSeismic), octree-local models (HiHa), minibatch VI (BayesNF)Global, multi-decade, multi-variable fields are mostly out of reach for one INR
UncertaintyBayesNF (priors + ensembles), Bayesian IntraSeismic (VI)GP links (NTK, OI equivalence) understood but rarely used in deployed INRs
Generalization across samplesFuncta, COIN++, CORAL modulations; applied: PINROD, multi-altitude LIIF, ClimplicitAmortized encoders trained on real observation data
Foundation modelsAurora and GraphCast decode to fixed grids; MLP heads on frozen Aurora latents are patch decodersCoordinate-queried continuous decoders (LIIF/INR heads) on foundation latents
Atmospheric compositionMethane, NO₂, XCO₂ gap-filling uses CNN, LSTM, U-Net, trees, diffusionNo neural-field work found; averaging-kernel-aware observation operators untouched

Software landscape

LibraryFrameworkWhat it gives
google/bayesnfJAXBayesian spatiotemporal neural fields, MAP/VI ensembles
DIFFICE-jaxJAXIce-shelf PINNs (SSA), viscosity inversion
PINNICLEDeepXDE (TF / PyTorch / JAX)Ice-sheet forward and inverse PINNs
DeepMind functaJAXMeta-learned latent modulations
MarcCoru/locationencoderPyTorchSpherical harmonics + SIREN location encoders
TorchSpatialPyTorchLocation-encoder zoo
ClimplicitPyTorchPretrained climate implicit embeddings
CORAL, AROMAPyTorchINR operator learning and latent dynamics
IceSheetReconstructionPyTorch + NextflowCryoSat-2 elevation INR pipeline

The benchmarks are OceanBench (SSH), FAIR-Earth (stratified fairness of Earth INRs), and SDRBench-style comparisons against SZ3, ZFP and MGARD.

Caveats

References
  1. Rußwurm, M., Klemmer, K., Rolf, E., Zbinden, R., & Tuia, D. (2024). Geographic Location Encoding with Spherical Harmonics and Sinusoidal Representation Networks. International Conference on Learning Representations (ICLR). https://github.com/MarcCoru/locationencoder
  2. Cai, & Balestriero, R. (2025). No Location Left Behind. International Conference on Learning Representations (ICLR). https://mlanthology.org/iclr/2025/cai2025iclr-location/
  3. Huang, L., & Hoefler, T. (2023). Compressing Multidimensional Weather and Climate Data into Neural Networks. International Conference on Learning Representations (ICLR). https://arxiv.org/abs/2210.12538
  4. Xu, & others. (2025). HiHa: Hierarchical Harmonic Decomposition to Implicit Neural Compression for Atmospheric Data. Computers & Geosciences. https://arxiv.org/abs/2411.06155
  5. Mostajeran, Pawar, Villarreal, & Faroughi. (2025). Context-aware implicit neural representations to compress Earth system model data. Scientific Reports, 15, 25932. https://www.nature.com/articles/s41598-025-11092-w
  6. Abdul Qayyum, Luo, Urban, Qian, & Yoon. (2024). Implicit Neural Representations for Simultaneous Reduction and Continuous Reconstruction of Multi-Altitude Climate Data. IEEE International Workshop on Machine Learning for Signal Processing (MLSP). https://arxiv.org/abs/2409.17367
  7. Hybrid Neural Representations for Spherical Data. (2024). https://arxiv.org/abs/2402.05965
  8. Dollinger, Robert, Plekhanova, Drees, & Wegner. (2025). Climplicit: Climatic Implicit Embeddings. https://arxiv.org/abs/2504.05089
  9. ImplicitTerrainV2. (2026). https://arxiv.org/html/2605.22556
  10. Can Deep Neural Networks Improve Compression of Very Large Scientific Data? (2026). https://arxiv.org/html/2606.14353
  11. Mirowski, P., & others. (2024). Neural Compression of Atmospheric States. https://arxiv.org/abs/2407.11666
  12. Gomes, & others. (2025). Lossy Neural Compression for Geospatial Analytics: A Review. https://arxiv.org/abs/2503.01505
  13. Johnson, J. E., & others. (2022). Neural Fields for Fast and Scalable Interpolation of Geophysical Ocean Variables. NeurIPS Workshop on Machine Learning and the Physical Sciences. https://arxiv.org/abs/2211.10444
  14. Johnson, J. E., Febvre, Q., Gorbunova, A., Metref, S., Ballarotta, M., Le Sommer, J., & Fablet, R. (2023). OceanBench: The Sea Surface Height Edition. Advances in Neural Information Processing Systems 36, Datasets and Benchmarks Track. https://proceedings.nips.cc/paper_files/paper/2023/file/f6ccbf94fa57c2ae372ece91b537574d-Paper-Datasets_and_Benchmarks.pdf
  15. Luo, & others. (2024). Continuous Field Reconstruction from Sparse Observations with Implicit Neural Networks. International Conference on Learning Representations (ICLR). https://arxiv.org/abs/2401.11611
Benchmarking
17 · The six-step cycle
Notes
Background