Excited that PosteriorBench has been accepted to NeurIPS 2026 🔥 Single reconstruction is not enough; Posterior recovery matters for scientific inverse solvers ⛰️ Welcome to benchmark your methods here!

PosteriorBench: going beyond point reconstructions for scientific inverse-problem to full posterior distributions. Many scientific problems involve indirect or partial observations. Multiple physical fields can explain the same measurements. A solver should capture these possibilities, yet reconstruction accuracy alone is misleading. We spent substantial compute to construct high-fidelity reference posteriors across four tasks: Darcy flow inversion, Poisson source recovery, carbon capture and storage, and light transport material inference. These reference data let researchers directly evaluate their solvers using five complementary metrics. One of our key findings: better reconstruction accuracy can coincide with worse posterior recovery. Even strong generative samplers struggle to get both the mean and variance right, often underestimating the uncertainty. Paper: Code: Thanks to Jiachen Yao, Sean Hsu, Xi Deng, and all our coauthors for making this work possible @Caltech #AIforScience# #InverseProblems# #UncertaintyQuantification#

Excited to share that I’ll be attending the SIAM Conference on Uncertainty Quantification (UQ26) this year! 🎙️ At the conference, I will deliver an invited talk on Physics-Informed Posterior Sampling for Scientific Inverse Problems. Time: Tuesday 3 PM Link: Many scientific inverse problems ask us to reconstruct complex hidden fields from sparse, noisy observations. In these settings, a single best guess is often not enough. What we really need is a way to generate solutions that are both uncertainty-aware and faithful to the underlying physics. 💫 In this talk, I'll present a central message: Function-space diffusion can serve as a foundation for posterior sampling; decoupling prior and physics fixes the low-data bottleneck; and the resulting framework works in realistic scientific applications with verified posterior. I’m especially looking forward to sharing and learning new theories and advances. 🧸 If you’re attending UQ26, I would love to connect! #ScientificMachineLearning# #UncertaintyQuantification# #InverseProblems# #DiffusionModels# #PhysicsInformedAI# #BayesianInference# #MachineLearning#

I found that Adam variants perform the best when beta_1=beta_2 in my work on optimizers for physics-informed neural networks (PINNs). And I'm glad to see that people have also found this secret sauce for Adam, on a wider domain. Setting beta_1 equal to beta_2 aligns the momentum tracking history length, stabilizing the scale. (especially when the loss surface is changing a lot) It also puts less penalization on the gradient norm, making the gradients larger, thus converging faster. ⏩Table 4 in this PINN literature: ⏩Newer literatures:

Accurate modeling of CO₂ storage in the subsurface is a critical challenge for scaling Carbon Capture and Storage (CCS). 🌎 But here’s the catch: the inverse problem (recovering geological properties from sparse field observations) is severely ill-posed. 🤒 Traditional approaches either struggle with the scarcity of measured data or are too computationally expensive. 💸 In our new work, we introduce Fun-DDPS (Function-space Decoupled Diffusion Posterior Sampling), a generative framework that decouples the problem into two parts: a function-space diffusion model that learns a prior over geological parameters, and a differentiable Local Neural Operator surrogate for physics modeling and conditioning. ✨ Why does the decoupling matter? The diffusion prior handles the heavy lifting of recovering missing geological information, while the neural operator surrogate makes data assimilation fast and physically grounded — no expensive full-physics simulations in the loop. Key results on synthetic CCS datasets: ⏩ 11x improvement in forward modeling with only 25% observations ✅ Robust inverse modeling for data assimilation under sparse, noisy conditions 🔥 First rigorous validation of diffusion-based inverse solvers against asymptotically exact Rejection Sampling (RS) posteriors This points toward a scalable, practical path for uncertainty-aware subsurface characterization — something the CCS community needs as projects move from pilots to full-scale deployment. 📷 Huge kudos to my amazing collaborators — this work wouldn’t have been possible without them: @IsaacJu13 @AnimaAnandkumar Sally M Benson @ggg_www_ #CarbonCapture# #CO2Sequestration# #MachineLearning# #DiffusionModels# #NeuralOperators# #AI4Science# #CCS# #Sustainability#

How do we solve PDE inverse problems with only 1% data? (That's just 500 pairs!) 📉 Joint models fail to provide sufficient guidance, while DDIS bypasses this by explicit forward modeling. ✨ Check out Appendix A for a deep dive into our design rationale. 🧠 Code coming soon!💻

2025 was a whirlwind of activity in AI+science. Our team’s seminal contributions to the field were well recognized and we deepened those foundations. You can read the year end summary here

Our AI+Science group from @Caltech has a number of papers at @NeurIPSConf in chronological order: FunDPS: Guided Diffusion Sampling on Function Spaces with Applications to PDEs R-KV: Redundancy-aware KV Cache Compression for Reasoning Models Friday 11:00-2:00pm NOBLE -- Neural Operator with Biologically-informed Latent Embeddings to Capture Experimental Variability in Biological Neuron Models Friday 4:30-7:30pm Workshops: Sparse autoencoder neural operators: Model recovery in function spaces Saturday 11:00-noon (oral), 15:45-17:00 (poster), Upper Level Ballroom 20D Geometric Operator Learning with Optimal Transport From Black Hole to Galaxy: Neural Operator Framework for Accretion and Feedback Dynamics Saturday 11:00-noon, Upper Level Ballroom 6CF Fourier Neural Operators for Fast Simulation and Inverse Design of Second-Harmonic Generation in TFLN Waveguide Inverse Design with Fourier Neural Operators for Quantum System Control Saturday 2:30-3:30pm, Upper Level Ballroom 6CF AI-Driven Mathematical Discovery for the Andrews–Curtis Conjecture LeanDojo-v2: A Comprehensive Library for AI-Assisted Theorem Proving in Lean Saturday 3:30 pm, Upper Level Ballroom 6A Coarse-to-Fine 3D MRI Reconstruction via 3D Neural Operators. Saturday 3:00-3:45pm, Upper level Rm 32AB M+Adam: Stable Low-Precision Training with Combined Adam--Madam Updates Saturday 3:00pm, Upper Level Ballroom 20A Flow-Guided Neural Operator for Self-Supervised Learning on Time Series Data Sunday 9:50am, Rm 28 A-E

🚀 We’re thrilled to announce the upcoming AI & Scientific Discovery online seminar! We have an amazing lineup of speakers. This series will dive into how AI is accelerating research, enabling breakthroughs, and shaping the future of research across disciplines.

🚨We propose EquiReg, a generalized regularization framework that uses symmetry in generative diffusion models to improve solutions to inverse problems. Aditi Chandrashekar, @rzirvi13, @AbbasMammadov11, @jiacheny7, @ZweiWang292206 , @AnimaAnandkumar 1/

Excited to introduce our latest work, Guided Diffusion Sampling on Function Spaces (FunDPS) ( - a discretization-agnostic generative framework for solving PDE-based forward and inverse problems. Diffusion-based posterior sampling on function spaces: Our model recovers full-field PDE solutions, coefficient functions, and boundary conditions from severely sparse (just 3%) measurements, yielding SotA performance in both speed and accuracy. Multi-resolution operator learning pipeline: FunDPS leverages Gaussian Random Field priors and neural operator architectures, enabling multi-resolution training and inference, reducing training time by 25% and inference time by 50%. Infinite-dimensional Tweedie’s Formula: We extend Tweedie’s formula into infinite-dimensional Banach spaces, forming the rigorous theoretical foundation for posterior mean estimation. Results: Achieved an average 32% accuracy improvement and 4x fewer sampling steps compared to previous SOTA approaches across five challenging PDE tasks. Plus, our multi-resolution inference pipeline accelerates computations by up to 25x! Paper ( Code ( based on our earlier workshop paper ( @jiacheny7, @AbbasMammadov11, @julberner, @gavinkerrigan, Jong Chul Ye, @Azizzadenesheli #DiffusionModels# #InverseProblems# #PDE# #MachineLearning# #NeuralOperators# #AI4Science#

🚀Thrilled to present PINNacle at #NeurIPS2024#! 🌍 📍Poster Location: West Ballroom, #5307#, 11am 🔑Highlights: - A comprehensive benchmark for Physics-Informed Neural Networks (PINNs). - Evaluates 10+ SOTA PINN methods on 20+ challenging PDE problems and more! Let's connect! #AI#

People with the most to teach live like they have the most to learn — and Steve loved learning. He was the most curious person I’ve ever met, which made him the best teacher I’ve ever known. Happy birthday, my friend.