Research map / Probabilistic and scientific modeling
Differential equations and PDEs: research map
614 accepted papers on Differential equations and PDEs in Probabilistic and scientific modeling, from ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026), grouped into 2 clusters and 7 approaches. The busiest year so far is 2026.
Within Probabilistic and scientific modeling, its share grew from 8.8% in 2023–24 to 9.8% in 2025–26 (178 → 299 papers at ICML, NeurIPS, CVPR and AAAI, the venues with data for all four years).
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Approaches and key papers
pde · physics · partial differential · 446 papers
Approaches in this cluster:
- Neural PDE solvers (135 papers)
Solves PDEs with convergence guarantees, coarse correction and latent spectral models. - Physics-informed operator learning (129 papers)
Embeds physical constraints in DeepONets and diffusion models for fluid and graph PDEs. - Neural operators for general geometries (111 papers)
Learns PDE solution operators on irregular domains using neural fields and latent operators. - Physics-informed neural network training (71 papers)
Improves PINN training through sequential, accelerated and competitive learning.
Most cited and most cited since 2024:
- Fourier Neural Operator for Parametric Partial Differential Equations (ICLR 2021 · 1,068 citations)
- Implicit Neural Representations with Periodic Activation Functions (NeurIPS 2020 · 262 citations)
- Fourier Neural Operator with Learned Deformations for PDEs on General Geometries (NeurIPS 2024 · 150 citations)
- Challenges in Training PINNs: A Loss Landscape Perspective (ICML 2024 · 40 citations)
ordinary · odes · differential equations · 168 papers
Approaches in this cluster:
- Neural ODE training and analysis (80 papers)
Study and speed up neural ODEs through adaptive control, theory, and simulation-free training. - Probabilistic inference for ODEs and SDEs (59 papers)
Estimate parameters and solutions of differential equations with probabilistic solvers and state-space inference. - Structured continuous-depth models (29 papers)
Build continuous-depth and differential-equation-based networks with conservation, sparsity, or higher-order structure.
Most cited and most cited since 2024:
- Neural Ordinary Differential Equations (NeurIPS 2018 · 558 citations)
- DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps (NeurIPS 2022 · 284 citations)
- Signed Graph Neural Ordinary Differential Equation for Modeling Continuous-Time Dynamics (AAAI 2024 · 14 citations)
- Neural Variable-Order Fractional Differential Equation Networks (AAAI 2025 · 9 citations)
Related topics in Probabilistic and scientific modeling
- Dynamical systems (969)
- Uncertainty and Gaussian processes (1,162)
- Molecules and proteins (1,990)
- Variational and generative sampling (2,060)
- Treatment effects (421)
- Causal discovery (830)
- Bayesian optimization (397)