The numbers landed without fanfare in a Stanford preprint this February. A new modeling system called Fun-DDPS—ungainly acronym and all—had achieved 7.7% relative error using just a quarter of available observations. Standard methods? 86.9% error.
That kind of gap doesn't happen often in subsurface engineering. And it arrives at a moment when carbon capture has stopped being a curiosity.
Consider: The Global CCS Institute counted 77 operational carbon storage projects worldwide as of 2025, a 54% jump in twelve months. Norway's Northern Lights consortium began injecting CO2 beneath the North Sea in August. Heidelberg Materials started pulling emissions from a cement plant in Brevik, Norway, that same spring—one of the first commercial-scale installations capturing process emissions that can't simply be electrified away. ExxonMobil is lining up storage contracts across the Gulf Coast. This isn't pilot-scale anymore.
Which means the industry suddenly needs modeling tools that don't just work in theory. They need to work Monday morning, when an operator is trying to decide injection rates for the next six months.
The Instrumentation Deficit
Here's the core problem, one that geoscientists have been wrestling with for decades: subsurface storage sites are profoundly under-instrumented. You drill wells, expensive ones, and you get snapshots—pressure readings, maybe some seismic imaging if budgets allow. From this sparse patchwork, you're supposed to predict how millions of tonnes of supercritical CO2 will behave in rock formations over timescales measured in decades.
Classical reservoir simulators grind through the physics. They're accurate, more or less. They're also glacial—hours or days for a single run. That makes the real work of uncertainty quantification, adjusting historical models to match field data, or anything approaching real-time monitoring... well, let's call it aspirational. At scale, it's borderline intractable.
Neural operators have been chipping away at this constraint. A 2023 paper in Energy & Environmental Science demonstrated basin-scale modeling with roughly 700,000-fold speedup versus conventional approaches. NVIDIA built accessible frameworks—PhysicsNeMo, Modulus—that helped bring these surrogates out of the lab. But speed alone doesn't solve the harder inverse problem lurking beneath: given sparse, noisy observations from a few wells, what can you actually infer about subsurface properties and future CO2 plume migration? What do you know, and what are you guessing?
That's where function-space diffusion enters the picture.
Learning Priors in Continuous Space
The Fun-DDPS approach, developed by Xin Ju, Jiachen Yao, Anima Anandkumar, Sally M. Benson, and Gege Wen, takes a different path. It learns a prior distribution over geological parameters not on fixed grids, but in function space—continuous representations that don't depend on how finely you've discretized your model. Pair that with what they call a Local Neural Operator, which acts as a physics surrogate, and you get a system that guides generation through actual subsurface physics rather than pattern-matching alone.
The practical difference? With sparse observations, Fun-DDPS generates posterior samples that match gold-standard rejection-sampling methods (Jensen-Shannon divergence below 0.06) while being roughly four times more sample-efficient. It suppresses high-frequency artifacts that plague simpler joint diffusion models—those visual glitches that might look plausible but violate conservation laws or boundary conditions.
This isn't just academic refinement. It's the gap between a prediction that looks good in a slide deck and one an operator can actually trust when deciding whether to increase injection pressure.
The broader lineage of function-space methods—FunDPS, FunDiff, and variants—has been validated across multiple partial differential equation domains with observation sparsity down to 3%. These are the same equations governing subsurface flow. Which suggests the approach might survive contact with reality.
Production Systems, Not Demos
And reality is moving fast. TGS, the Norwegian geoscience data company, integrated its Prediktor Data Gateway with Equinor's Northern Lights operations last July—managing simulation, capacity planning, CO2 tracking, and regulatory reporting in a unified system. Not a prototype. A production deployment.
Schlumberger launched Lumi, its AI-powered data platform, and is working with Shell and Aker BP on what they're calling "agentic-AI" for subsurface automation. CGG partnered with Baker Hughes to offer turnkey CCS services from site screening through long-term monitoring. Earth Science Analytics, a smaller Norwegian firm, is using its EarthNET platform for 3D property prediction and uncertainty quantification on live projects, including work with Horisont Energi up in the Barents Sea.
These aren't research demonstrations. They're tools being deployed to screen sites, design injection strategies, and monitor containment in real time. The lag between academic breakthrough and commercial use is shrinking, maybe faster than the industry expected.
Policy as Forcing Function
Part of what's pushing this along—maybe more than engineers want to admit—is policy. Messy, imperfect policy, but policy nonetheless.
The U.S. Inflation Reduction Act bumped the 45Q tax credit to $85 per tonne for qualifying projects. Texas gained Class VI permitting authority last November, joining five other states and potentially shaving months off approval timelines. The EU's Net-Zero Industry Act mandates 50 million tonnes per year of operational injection capacity by 2030, with specific obligations on oil and gas producers who helped create the problem.
Canada is offering investment tax credits up to 60% for direct air capture equipment. Northern Lights issued its first storage certificates in December—a verification model that others will likely copy, creating a forcing function for rigorous, auditable modeling. ExxonMobil's Low Carbon Solutions unit reports contracts for roughly 16 million tonnes annually. CF Industries brought its Donaldsonville, Louisiana, facility online at about 2 million tonnes per year.
The IEA's pipeline analysis suggests 430 million tonnes per year of capture capacity by 2030. Still below net-zero pathways, but growing fast enough to stress every assumption about how to characterize sites, model plume behavior, and manage reservoir pressure.
Where Risk Becomes Quantifiable
Which brings us to why AI shifts from convenience to critical infrastructure.
Sally M. Benson, one of the Fun-DDPS co-authors and a CCS researcher for decades, has described the sector's evolution from "nice to have" to "inevitable." That inevitability imposes hard constraints. Over-inject and you risk fracturing the caprock that's supposed to seal in your CO2. Under-inject and you waste expensive capture capacity that your offtakers are paying for. Misjudge plume migration and regulators start asking uncomfortable questions.
Digital twins—systems integrating well data, 4D seismic, satellite-based deformation monitoring, and Bayesian inference—are edging toward real-time control of injection parameters. But those systems need fast forward models and credible uncertainty bounds. That's the promise of marrying operator-learning surrogates with function-space generative models: speed, physics consistency, and rigorous validation in one package.
Rakesh Jaggi, president of SLB Digital, talks about AI "reshaping subsurface workflows." It's perhaps more mundane than that. AI is becoming the actuarial layer for geological risk—the mechanism that lets you write contracts, secure project finance, and satisfy regulators that you genuinely know where the CO2 will go.
The Rough Edges
Challenges? Plenty. Class VI permitting still carries federal backlogs; even with state primacy, figure 18 to 24 months per well. CO2 pipeline routing faces local opposition—South Dakota regulators denied Summit Carbon Solutions' permits last April, and Navigator canceled its Heartland Greenway project back in 2023 after similar pushback. The Pipeline and Hazardous Materials Safety Administration proposed stricter safety regulations in January 2025, responding to incidents like the 2020 Satartia, Mississippi rupture that hospitalized dozens. Those rules, if finalized, will add cost and complexity.
There's also the performance gap between pilot projects and commercial scale. Critics regularly cite Chevron's Gorgon facility in Australia, which has consistently underperformed its capture targets. Northern Lights and Brevik are being scrutinized precisely because they're among the first real tests of whether European hub-and-spoke models can deliver what the spreadsheets promise.
And then there's deployment risk for the AI itself. Fun-DDPS and similar methods remain research-stage. Translating them into production workflows at Northern Lights, at Rotterdam's Porthos project (targeting 2026 operations), or across Gulf Coast hubs will require validation campaigns, software integration, and training operators who may not have machine learning backgrounds. NVIDIA's platforms lower some barriers, but subsurface AI is still a specialist's domain.
Eighteen Months Out
A few things to watch.
First, whether operators managing large-scale injection—Northern Lights ramping toward 5 million tonnes per year after its Phase 2 investment decision in March, or Porthos aiming for 2.5 million tonnes annually—begin deploying function-space or operator-learning models in monitoring workflows. Not as experiments. As standard practice.
Second, whether measurement, reporting, and verification gets digitized across projects. If Northern Lights' storage certificate model spreads, that creates pressure for rigorous, auditable modeling everywhere. Can't fake your way through an audit with a surrogate model that doesn't respect physics.
Third, whether U.S. Gulf Coast hubs—where TGS is already providing storage assessments and ExxonMobil is aggregating customers—adopt AI-driven site characterization tools. The Gulf Coast could become the proving ground simply by virtue of scale and urgency.
The Global CCS Institute's Jarad Daniels emphasized last year that sustaining momentum requires "durable policy, finance, and infrastructure." AI is quietly slipping into that third category—not the capture technology itself, but the modeling and assurance layer that makes the rest bankable.
A 90% reduction in prediction error isn't merely an academic milestone. It's the kind of improvement that changes which projects secure financing, which applications regulators approve, and what the industry can credibly commit to delivering.
Whether that's sufficient to close the yawning gap between current trajectories and net-zero pathways remains unsettled. But the tools to answer that question with precision are arriving faster than most anticipated. Sometimes, infrastructure gets built in unexpected places.
