Overcoming Data Limitations In AI Model Development

How do we bring AI to scientific modeling? The standard approach has been AI to augment existing numerical simulations. In a new work https://lnkd.in/gFMUvUbB we show this approach is fundamentally limited. In contrast, using the end-to-end AI approach of Neural Operators to completely replace numerical solvers helps overcome this limitation both in theory and in practice. Current augmentation approaches use AI as a closure model while keeping a coarse-grid numerical solver in the loop. We show that such approaches are generally unable to reach full fidelity, even if we make the closure models stochastic, providing them with history information and even unlimited ground-truth training data from full-fidelity solvers. This is because the closure model is forced to be at the same coarse resolution as the (cheap and approximate) numerical solver, and their combination does not result in high-fidelity solutions. In contrast, Neural Operators do not suffer from this limitation since they operate at any resolution and learn the mapping between functions. Neural Operators are first trained on coarse-grid approximate solvers, since we can generate lots of training data, and only use a small amount of expensive data from high-fidelity solvers in addition to physics-based losses to fine-tune the Neural Operator model for strong generalization. The key is that the Neural Operator model operates on any resolution, and can thus, accept data at multiple resolutions for training efficiently, without burdensome data-generation requirements.  Thus, Neural Operators fundamentally change how we apply AI to scientific domains.

The places where AI Agents are most beneficial are the places where sourcing the data is harder to find and more costly and time consuming to collect: SME knowledge transfer. Companies around the country have SMEs that are simply overwhelmed by their workflow, don’t have the time for knowledge transfer and require tools to take the repetitive tasks off of their plate so they can be more productive. This is where AI Agents can come in: - They shine where data is scarce and costly to collect - They can handle repetitive tasks, freeing up SMEs for high-value work - They can facilitate knowledge transfer without overburdening experts The challenge? - Data Limitations: SME knowledge is irreplaceable and, as a result, not available online. It’s imperative that devs involve SMEs in the development process while prioritizing the SME’s schedule. Why?  - Calibration is Crucial: AI Agents that do not align with the SME will return irrelevant and useless results wasting time and money. How? - Human-in-the-Loop techniques: Direct SME involvement in calibration yields the best results. Their input fine-tunes AI responses and decision-making. AND - Iterative Improvement: Calibration must be ongoing. Regular feedback loops between AI and SMEs drive continuous enhancement. What does this do? - The AI solution will be built as complement, not replacement, to Human ability:. The goal is to augment SME capabilities, not replace them. This synergy boosts productivity and knowledge sharing. While initial calibration takes time, the long-term gains in efficiency and knowledge dissemination are well worth it. AI Agents can be built responsibly while including our SMEs and improving performance. It takes true engineering and ingenuity to allow AI to move us forward and not replace invaluable talent. 

In a previous discussion, we explored the No-Free-Lunch Theorem, which tells us there is no universally best model for all problems. The key takeaway was that domain knowledge can guide us in inducing the right bias into our models, especially in fields like engineering and physics, where we often have extensive domain expertise but limited data. I proposed three strategies for tackling this challenge: 1. 𝗚𝗲𝘁 𝗠𝗼𝗿𝗲 𝗗𝗮𝘁𝗮: The straightforward approach, but not always feasible. 2. 𝗜𝗻𝗱𝘂𝗰𝗲 𝗯𝗶𝗮𝘀 𝗜𝗡𝗧𝗢 𝘁𝗵𝗲 𝗱𝗮𝘁𝗮: Leveraging domain knowledge to shape model behavior. 3. 𝗠𝗼𝗱𝗶𝗳𝘆 𝘁𝗵𝗲 𝗼𝗯𝗷𝗲𝗰𝘁𝗶𝘃𝗲 𝗳𝘂𝗻𝗰𝘁𝗶𝗼𝗻: Adjusting the model's training target to favor desired solutions. Physics-Informed Neural Networks (PINNs) are a perfect example of the third strategy: modifying the objective function to induce a bias. Let’s dive into how this works using the viral simple harmonic oscillator as an example. 𝗪𝗵𝘆 𝗠𝗼𝗱𝗶𝗳𝘆 𝘁𝗵𝗲 𝗢𝗯𝗷𝗲𝗰𝘁𝗶𝘃𝗲 𝗙𝘂𝗻𝗰𝘁𝗶𝗼𝗻? In the illustration, we see two models trained on the same problem: a vanilla neural network and a PINN. Both models aim to predict the behavior of a harmonic oscillator based on limited examples. During training, both models match the training data exactly. However the PINN has a modified objective function; not only does it minimize the MSE loss, but the network is also regularized with an additional objective to minimize the harmonic oscillation function based on derivatives of the output as additional constraints. That's why the model trains longer than the vanilla neural network. 𝗔 𝗗𝗶𝗳𝗳𝗲𝗿𝗲𝗻𝘁 𝗞𝗶𝗻𝗱 𝗼𝗳 𝗢𝗽𝘁𝗶𝗺𝗶𝘇𝗮𝘁𝗶𝗼𝗻 While it might seem like the neural network and the PINN are solving the same problem, they are actually optimizing different objectives. The PINN doesn't just try to fit the data; it also ensures the model follows our bias of generating results that follow physical laws. This added constraint changes the optimization landscape, leading the model to a more physically consistent solution. The resulting predictions are far more accurate for cases where data is scarce or noisy. 𝗥𝗲𝗮𝗹-𝗪𝗼𝗿𝗹𝗱 𝗔𝗽𝗽𝗹𝗶𝗰𝗮𝘁𝗶𝗼𝗻𝘀 𝗮𝗻𝗱 𝗟𝗶𝗺𝗶𝘁𝗮𝘁𝗶𝗼𝗻𝘀 In practice, I've never seen a PINN in production. However, the principle of regularizing models with additional constraints is widely used across various domains. For instance, adding penalty terms to enforce business preferences, smoothness, boundary conditions, or physical laws can significantly improve model generalization. The core idea remains the same: by modifying the objective function to include domain-specific constraints, we can induce a bias to guide our models toward better solutions, even when data is limited. It’s a strategy worth considering in any situation where domain knowledge provides insights into the desired behavior of a system. #DSwithSaul #PhysicsInformedNeuralNetworks #PINN

If you're working on AI projects with limited training data, building domain-specific AI applications, or struggling with the economics of data labeling, you should know about this new approach from the DeepSeek team. Reinforcement Fine-Tuning (RFT) is a new technique for fine-tuning large language models, cutting the required labeled data from thousands to just tens of examples. Traditional supervised fine-tuning (SFT) approaches have always been hampered by their dependence on vast amounts of labeled data. RFT takes a fundamentally different approach by utilizing a reward function to evaluate response correctness, enabling the model to learn more effectively than through simple mimicry of examples. The same technique that was used to develop DeepSeek-R1. This method proves particularly powerful in three key scenarios: (1) When no labeled data exists but correctness can be verified - such as code transpilation where outputs can be automatically tested. (2) When only limited labeled examples are available - fewer than 100 examples, where traditional methods typically overfit. (3) For tasks that benefit from chain-of-thought reasoning - where step-by-step logical thinking significantly improves results. A well-written post from Predibase here (they also added support for RFT on their platform recently!) https://lnkd.in/gHBdW5De P.S. Predibase just released an open-source model that outperforms OpenAI o1 by 67% for PyTorch-to-Triton transpilation tasks, enabling more efficient and intelligent AI models (link in comments).