⚡ electrical engineering

Virtual Sensing to Enable Real-Time Monitoring of Inaccessible Locations & Unmeasurable Parameters

This paper introduces MIMONet, an operator-based virtual sensing framework that leverages neural operators to achieve real-time, mesh-independent inference of inaccessible internal thermal-fluid fields in safety-critical energy systems from sparse boundary measurements, overcoming the limitations of existing state estimation methods while maintaining high accuracy and robustness under noise.

Original authors: Kazuma Kobayashi, Farid Ahmed, Jaewan Park, Subhankar Sarkar, Souvik Chakraborty, Syed Bahauddin Alam

Published 2026-06-16

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Kazuma Kobayashi, Farid Ahmed, Jaewan Park, Subhankar Sarkar, Souvik Chakraborty, Syed Bahauddin Alam

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to understand what's happening inside a sealed, super-hot, radioactive nuclear reactor. You can't stick a thermometer or a pressure gauge inside because the radiation would destroy the sensor instantly, and the heat would melt it. Yet, knowing the temperature and pressure inside is critical for safety.

This paper introduces a clever solution called "Virtual Sensing." Instead of trying to build a better physical sensor, the researchers built a "digital mind" that can guess the entire internal state of the reactor just by looking at a few clues on the outside.

Here is how it works, broken down with simple analogies:

1. The Problem: The "Black Box" Reactor

Think of a nuclear reactor like a sealed, glowing black box.

The Reality: You can only measure things on the outside (like the speed of water entering the box or the heat coming out).
The Danger: Inside, the water swirls, heats up, and creates pressure in complex ways. If you don't know what's happening inside, you can't be sure the reactor is safe.
The Old Way: Scientists used to run massive, slow computer simulations to guess what's inside. But these simulations take hours to run. By the time they finish, the reactor's conditions have already changed. It's like trying to navigate a storm by looking at a weather map from yesterday.

2. The Solution: The "Digital Twin" Mind

The researchers created a new type of AI called MIMONet. Think of this AI as a super-intuitive chef.

The Analogy: Imagine a chef who has never seen the inside of a pot of soup. However, they have tasted thousands of soups where they knew exactly how much salt, heat, and stirring went in (the "boundary" clues).
The Magic: Because the chef has learned the rules of how soup behaves, if you tell them, "I added 2 cups of broth and turned the heat to high," they can instantly describe exactly how the soup is swirling, where the hot spots are, and how fast it's boiling inside the pot—even though they can't see inside.
The Paper's Claim: MIMONet learns the "rules of physics" (the laws of fluid flow and heat) from high-quality computer simulations. Once trained, it can look at sparse, noisy data from the reactor's exterior and instantly reconstruct a full, 3D picture of the invisible interior.

3. How It's Different from Old AI

Previous AI models were like spot-checkers. If you asked them, "What is the temperature at this specific point?" they could guess. But if you moved the point, they had to relearn or guess blindly. They couldn't see the whole picture.

MIMONet is different. It doesn't just guess a single number; it learns a continuous map.

The Analogy: Instead of guessing the temperature at one spot, MIMONet draws a complete, smooth heat-map of the entire reactor interior. You can ask it, "What's the pressure at any point inside?" and it answers instantly, even if no sensor has ever been there.
Speed: It does this in milliseconds (faster than a human blink), whereas the old computer simulations took hours.

4. Testing the "Digital Mind"

The researchers tested this AI on three increasingly difficult scenarios to prove it works:

The Simple Box (Lid-Driven Cavity): A simple box where the top moves. The AI had to guess the swirling air inside just by watching the top move. It succeeded with very high accuracy.
The Narrow Channel (Reactor Subchannel): A tight space where water flows between fuel rods. It's impossible to put sensors in the gaps. The AI guessed the flow and heat perfectly just from the inlet conditions.
The Complex Machine (Heat Exchanger): A tangled system of pipes with heat and pressure interacting. This is the hardest test. The AI still managed to reconstruct the invisible pressure and flow patterns with less than 1% error.

5. Handling "Noisy" Data

In the real world, sensors aren't perfect; they get "jittery" or drift over time (like a shaky hand).

The Test: The researchers intentionally added "noise" (random errors) to the input data to see if the AI would panic.
The Result: A standard AI model would get confused and give wild guesses. MIMONet, however, used a special technique (called "Monte Carlo Dropout") to act like a committee of experts. Instead of one guess, it asked 20 slightly different versions of itself and averaged their answers. This made it incredibly stable, ignoring the sensor noise and still giving a reliable picture of the inside.

6. Knowing When It's Unsure

Finally, the paper explains that the AI knows when it's guessing.

The Analogy: If you ask the chef about a soup recipe they've never seen, they might say, "I'm 95% sure, but I'm a little nervous about this part."
The Reality: MIMONet provides a "confidence score." If the sensors are very noisy or the situation is weird, the AI highlights those areas as "uncertain." This is crucial for safety, so operators know where the AI is confident and where it needs more data.

Summary

This paper presents a breakthrough in Virtual Sensing. It proves that we can use a specialized AI (MIMONet) to "see" inside dangerous, inaccessible places like nuclear reactors. By learning the physics of how fluids and heat move, this AI can turn a few messy, outside measurements into a clear, real-time, 3D map of the invisible interior, doing it faster and more accurately than ever before. It's like giving the reactor a pair of "X-ray vision" glasses that don't require any physical sensors inside the box.

Technical Summary: Virtual Sensing for Real-Time Monitoring of Inaccessible Locations

Problem Statement
Next-generation nuclear reactors and other safety-critical energy systems face a fundamental "observability crisis." While these systems require real-time monitoring of internal states (pressure, temperature, flow) for safety assurance, direct physical instrumentation is often infeasible due to radiation damage, thermal limits, complex geometries, and mechanical fragility. Existing virtual sensing (soft sensing) approaches are insufficient for this domain:

Model-based methods (e.g., Kalman filters, Luenberger observers) rely on known governing equations and produce finite-dimensional state vectors at specific coordinates, failing to reconstruct continuous spatial fields in uninstrumented regions or guarantee cross-field coherence at millisecond latencies.
Data-driven methods (e.g., RNNs, GNNs, standard regression) typically output scalar values at fixed, pre-trained coordinates. They lack mesh independence, cannot reconstruct coherent spatial fields on arbitrary grids, and often require per-instance retraining, preventing real-time deployment.
Physics-Informed Neural Networks (PINNs) solve specific PDE instances via optimization, which is computationally too slow for continuous, low-latency monitoring compared to the required sub-millisecond inference.

The core challenge is to reconstruct full, coupled interior fields from sparse, heterogeneous boundary measurements in real time, without explicit governing equations at inference time, and with calibrated uncertainty for safety-critical decision-making.

Methodology: MIMONet
The authors propose MIMONet, a neural operator framework designed specifically for nuclear-grade virtual sensing. Unlike traditional regressors that map vectors to vectors, MIMONet learns a nonlinear operator $G: \mathcal{U} \to \mathcal{S}$ that maps input functions (boundary conditions, heat sources) to continuous output fields at arbitrary query coordinates.

Key architectural innovations include:

Multi-Modal Branch Encoders: The network accepts heterogeneous inputs, including both scalar parameters (e.g., inlet temperature) and function-valued fields (e.g., spatial heat flux profiles), encoding them into latent representations.
Multiplicative Branch Fusion: Instead of additive fusion, the latent representations are fused multiplicatively. This choice is explicitly designed to preserve the bilinear coupling structure inherent in the Navier-Stokes equations (e.g., advective and convective transport terms), ensuring physical coherence across coupled fields.
Shared-Latent Multi-Field Decoding: A single trunk network maps spatial query coordinates to decoding bases. All output channels (e.g., pressure, velocity components, temperature) share the same fused latent representation, differing only in their final per-channel basis projections. This enforces inter-field consistency and allows for the simultaneous reconstruction of multiple coupled physical quantities.

The framework is trained on high-fidelity CFD data (ANSYS Fluent) across three escalating scenarios:

Lid-Driven Cavity (LDC): A canonical flow with inaccessible internal recirculation zones, testing boundary-only inference.
PWR Subchannel Flow: A geometrically confined reactor subchannel with cross-stream mixing, testing inference in inaccessible, confined geometries.
Heat Exchanger: A fully coupled multiphysics system with tight pressure-velocity-temperature interdependencies, representing industrial-grade complexity.

Key Results
Evaluated on data-center accelerators (NVIDIA H200, A40, GH200), MIMONet demonstrates:

Accuracy: Relative $\ell_2$ errors of <5% across all three scenarios (e.g., 0.80% for pressure in the heat exchanger, 2.2% for velocity in the subchannel). This represents an order-of-magnitude improvement over baseline neural operators (GeoFNO, NOMAD, KCN) and classical regression methods.
Latency: Sub-millisecond inference times (e.g., 0.35 ms per heat-exchanger inference on an H200), enabling real-time monitoring loops.
Robustness: The model maintains stability under 50% sensor noise. While deterministic baselines degrade significantly (e.g., ~30–50% error increase), MIMONet utilizing Monte Carlo (MC) dropout ensembles maintains error inflation below 3%.
Uncertainty Quantification: By combining MC dropout with conformal prediction, the framework provides calibrated uncertainty estimates. Post-hoc calibration ensures that 95% prediction intervals achieve nominal coverage, offering statistically valid confidence bounds for inaccessible regions.
Generalization: The operator supports "mesh-independent" evaluation, allowing queries at arbitrary coordinates without retraining or regridding, even in regions physically disjoint from the sensor locations.

Significance and Claims
The paper claims that MIMONet establishes simulation-based feasibility for continuous, real-time monitoring of safety-critical energy systems where direct instrumentation fails. Its primary contributions are:

Paradigm Shift: Moving virtual sensing from pointwise scalar estimation to coherent, full-field reconstruction using operator learning.
Architectural Specificity: Demonstrating that specific architectural choices (multiplicative fusion, shared-latent decoding) are necessary to handle the coupled, multi-physics nature of nuclear thermal-fluid systems, which single-field operators cannot address.
Operational Viability: Proving that neural operators can achieve the "train-once, deploy-continuously" property required for real-time safety margins, offering a speedup of five to six orders of magnitude over high-fidelity CFD.

The authors position this work as a systematic application of neural operators to a domain previously unaddressed by published architectures in their single-field forms. They explicitly state that while the method is validated on high-fidelity simulations, future experimental and cross-solver validation is required before autonomous deployment in actual reactors. The work does not claim to replace physical sensors but to restore observability in regions where sensors are physically impossible to install.