Function graph transformers use graph measures to provide a measure-theoretic framework where standard transformer components universally approximate operators between function spaces while preserving single-valued function outputs.
Poseidon: Efficient foundation models for PDEs
11 Pith papers cite this work, alongside 9 external citations. Polarity classification is still indexing.
11
Pith papers citing it
9
external citations · external index
representative citing papers
OmniMol transfers a billion-jet pre-trained PET foundation model from HEP to molecular dynamics via an interaction-matrix attention bias, delivering strong performance on the oMol dataset with minimal fine-tuning and fast inference.
WLNO augments LNO with a parallel Haar wavelet branch and learnable gate to capture multi-scale spatial features, outperforming LNO on five PDE benchmarks especially those with sharp structures.
ARC-STAR reduces velocity rollout error by at least 36x over raw Poseidon across all tested regime cells via auditable global and local correction stages on five flow benchmarks.
A hybrid transformer-FEM integrator provides provable discrete energy preservation and gradient bounds for stable autoregressive forecasting of chaotic systems, with 65x fewer parameters and 9000x speedup in a fusion surrogate trained on 12 simulations.
SuperWing supplies 4,239 diverse wing shapes and 28,856 flow-field solutions that let Transformer models predict surface aerodynamics to 2.5 drag-count error and generalize zero-shot to DLR-F6 and NASA CRM wings.
ShockCast is a two-phase ML method that predicts adaptive timestep sizes to model high-speed flows with shocks more efficiently than fixed-step approaches.
SIGS is a neuro-symbolic framework that discovers analytical solutions to PDEs by generating grammar-constrained expressions, embedding them in a topology-regularised latent manifold, and refining structure and coefficients against the PDE residual and boundary/initial conditions.
Case study applies SAE probing with enstrophy triage to a continuum-dynamics foundation model and reports intermittent feature consistency that does not align with standard physics while linking some output discrepancies to specific feature changes.
Presents sequential physics-constrained neural operator models for the Norne reservoir with theoretical stability guarantees and empirical accuracy exceeding 0.99 R² for oil production predictions alongside a 10,000x computational speedup.
Scaling laws for weather models exhibit strong cross-channel and cross-horizon heterogeneity, where globally pooled metrics appear favorable while many individual channels degrade at longer leads.
citing papers explorer
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Function graph transformers universally approximate operators between function spaces
Function graph transformers use graph measures to provide a measure-theoretic framework where standard transformer components universally approximate operators between function spaces while preserving single-valued function outputs.
-
OmniMol: Transferring Particle Physics Knowledge to Molecular Dynamics with Point-Edge Transformers
OmniMol transfers a billion-jet pre-trained PET foundation model from HEP to molecular dynamics via an interaction-matrix attention bias, delivering strong performance on the oMol dataset with minimal fine-tuning and fast inference.
-
WLNO: Wavelet-Laplace Neural Operator for Solving Partial Differential Equations
WLNO augments LNO with a parallel Haar wavelet branch and learnable gate to capture multi-scale spatial features, outperforming LNO on five PDE benchmarks especially those with sharp structures.
-
ARC-STAR: Auditable Post-Hoc Correction for PDE Foundation Models
ARC-STAR reduces velocity rollout error by at least 36x over raw Poseidon across all tested regime cells via auditable global and local correction stages on five flow benchmarks.
-
A Hybridizable Neural Time Integrator for Stable Autoregressive Forecasting
A hybrid transformer-FEM integrator provides provable discrete energy preservation and gradient bounds for stable autoregressive forecasting of chaotic systems, with 65x fewer parameters and 9000x speedup in a fusion surrogate trained on 12 simulations.
-
SuperWing: a comprehensive transonic wing dataset for data-driven aerodynamic design
SuperWing supplies 4,239 diverse wing shapes and 28,856 flow-field solutions that let Transformer models predict surface aerodynamics to 2.5 drag-count error and generalize zero-shot to DLR-F6 and NASA CRM wings.
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A Two-Phase Deep Learning Framework for Adaptive Time-Stepping in High-Speed Flow Modeling
ShockCast is a two-phase ML method that predicts adaptive timestep sizes to model high-speed flows with shocks more efficiently than fixed-step approaches.
-
Neuro-Symbolic AI for Analytical Solutions of Differential Equations
SIGS is a neuro-symbolic framework that discovers analytical solutions to PDEs by generating grammar-constrained expressions, embedding them in a topology-regularised latent manifold, and refining structure and coefficients against the PDE residual and boundary/initial conditions.
-
Sparse probes and murky physics: a case study of interpretability challenges in a foundation model for continuum dynamics
Case study applies SAE probing with enstrophy triage to a continuum-dynamics foundation model and reports intermittent feature consistency that does not align with standard physics while linking some output discrepancies to specific feature changes.
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Sequential Physics-Constrained Neural Operator Forward Modeling for the $\textit{Norne}$ Reservoir System
Presents sequential physics-constrained neural operator models for the Norne reservoir with theoretical stability guarantees and empirical accuracy exceeding 0.99 R² for oil production predictions alongside a 10,000x computational speedup.
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Towards Scaling Law Analysis For Spatiotemporal Weather Data
Scaling laws for weather models exhibit strong cross-channel and cross-horizon heterogeneity, where globally pooled metrics appear favorable while many individual channels degrade at longer leads.