Uncertainty quantification is essential in safety-critical settings--from autonomous driving to aviation, finance, and health--where decisions must rely on conservative bounds rather than point estimates. Predictor-level intervals (e.g., from quantile regression, conformal prediction, variance networks, or Bayesian models) generally do not compose: adding two per-variable intervals need not yield a valid interval for their sum or preserve coverage. In aviation, Gaussian overbounding replaces complex error distributions with a conservative Gaussian whose tails dominate the truth, so conservatism propagates through linear operations. Yet classical overbounds are global, often overly conservative, and hard to adapt to feature-conditioned errors. We propose a unified learning framework that trains neural networks to produce context-aware Gaussian overbounds--mean and scale--with provable conservatism on a finite quantile grid and, under three explicit regularity assumptions, continuous-tail conservatism on a certified interval. Our overbounding loss enforces conservativeness at selected quantiles while penalizing distributional distance with a Wasserstein-style term. The learned bounds support conservative linear-combination and convolution analysis on the enforced grid, and on the certified interval when assumptions hold, while being less redundant than traditional methods. We provide a scoped analysis of discrete-to-continuous conservatism and compact-domain objective regularity, and validate on synthetic data and real-world datasets, including multipath, ionospheric, and tropospheric residual errors. Across these settings, the method yields tighter bounds while maintaining conservatism on the enforced grid and in experiments. The framework is modality-agnostic and applicable to learning systems that require conservative, feature-conditioned uncertainty estimates in dynamic environments.

In the first case, points arrive sequentially, and only a summary can be stored in memory.

Neural Information Processing Systems http://nips.cc/

The deviated model can be motivated by many applications in science.

It takes considerable resources to train complex models on a rich data population.

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The performance of machine learning surrogates is critically dependent on data quality and quantity. This presents a major challenge, as high-fidelity (HF) data is often scarce and computationally expensive to acquire, while low-fidelity (LF) data is abundant but less accurate. To address this data-scarcity problem, we develop a probabilistic multi-fidelity surrogate framework based on generative transfer learning. We employ a normalizing flow (NF) generative model as the backbone, which is trained in two phases: (i) the NF is first pretrained on a large LF dataset to learn a probabilistic forward model; (ii) the pretrained model is then fine-tuned on a small HF dataset, allowing it to correct for LF-HF discrepancies via knowledge transfer. To relax the dimension-preserving constraint of standard bijective NFs, we integrate surjective (dimension-reducing) layers with standard coupling blocks. This architecture enables learned dimension reduction while preserving the ability to train with exact likelihoods. The resulting surrogate provides fast probabilistic predictions with quantified uncertainty and significantly outperforms LF-only baselines while using fewer HF evaluations. We validate the approach on a reinforced concrete slab benchmark, combining many coarse-mesh (LF) simulations with a limited set of fine-mesh (HF) simulations. The proposed model achieves probabilistic predictions with HF accuracy, demonstrating a practical path toward data-efficient, generative AI-driven surrogates for complex engineering systems. Email address: David.Barajas-Solano@pnnl.gov (David Barajas-Solano) Introduction High-fidelity (HF) computer modeling using discretization schemes such as the finite elements (FE) method provides a rigorous framework for analyzing and predicting the behavior of complex engineering systems.

Double perovskites (DPs) are promising candidates for sustainable energy technologies due to their compositional tunability and compatibility with low-energy fabrication, yet their vast design space poses a major challenge for conditional materials discovery. This work introduces a multi-agent, text gradient-driven framework that performs DP composition generation under natural-language conditions by integrating three complementary feedback sources: LLM-based self-evaluation, DP-specific domain knowledge-informed feedback, and ML surrogate-based feedback. Analogous to how knowledge-informed machine learning improves the reliability of conventional data-driven models, our framework incorporates domain-informed text gradients to guide the generative process toward physically meaningful regions of the DP composition space. Systematic comparison of three incremental configurations, (i) pure LLM generation, (ii) LLM generation with LLM reasoning-based feedback, and (iii) LLM generation with domain knowledge-guided feedback, shows that iterative guidance from knowledge-informed gradients improves stability-condition satisfaction without additional training data, achieving over 98% compositional validity and up to 54% stable or metastable candidates, surpassing both the LLM-only baseline (43%) and prior GAN-based results (27%). Analyses of ML-based gradients further reveal that they enhance performance in in-distribution (ID) regions but become unreliable in out-of-distribution (OOD) regimes. Overall, this work provides the first systematic analysis of multi-agent, knowledge-guided text gradients for DP discovery and establishes a generalizable blueprint for MAS-driven generative materials design aimed at advancing sustainable technologies.