Benjamin Migliori

James Amarel, Robyn Miller, Nicolas Hengartner et al.

We study how neural emulators of partial differential equation solution operators internalize physical symmetries by introducing an influence-based diagnostic that measures the propagation of parameter updates between symmetry-related states, defined as the metric-weighted overlap of loss gradients evaluated along group orbits. This quantity probes the local geometry of the learned loss landscape and goes beyond forward-pass equivariance tests by directly assessing whether learning dynamics couple physically equivalent configurations. Applying our diagnostic to autoregressive fluid flow emulators, we show that orbit-wise gradient coherence provides the mechanism for learning to generalize over symmetry transformations and indicates when training selects a symmetry compatible basin. The result is a novel technique for evaluating if surrogate models have internalized symmetry properties of the known solution operator.

Tim Sainburg, Marvin Thielk, Brad Theilman et al.

We present a neural network architecture based upon the Autoencoder (AE) and Generative Adversarial Network (GAN) that promotes a convex latent distribution by training adversarially on latent space interpolations. By using an AE as both the generator and discriminator of a GAN, we pass a pixel-wise error function across the discriminator, yielding an AE which produces non-blurry samples that match both high- and low-level features of the original images. Interpolations between images in this space remain within the latent-space distribution of real images as trained by the discriminator, and therfore preserve realistic resemblances to the network inputs. Code available at https://github.com/timsainb/GAIA

Siddharth Mansingh, James Amarel, Ragib Arnab et al.

Partial Differential Equations (PDEs) are the bedrock for modern computational sciences and engineering, and inherently computationally expensive. While PDE foundation models have shown much promise for simulating such complex spatio-temporal phenomena, existing models remain constrained by the pretraining datasets and struggle with auto-regressive rollout performance, especially in out-of-distribution (OOD) cases. Furthermore, they have significant compute and training data requirements which hamper their use in many critical applications. Inspired by recent advances in ``thinking" strategies used in large language models (LLMs), we introduce the first test-time computing (TTC) strategy for PDEs that utilizes computational resources during inference to achieve more accurate predictions with fewer training samples and smaller models. We accomplish this with two types of reward models that evaluate predictions of a stochastic based model for spatio-temporal consistency. We demonstrate this method on compressible Euler-equation simulations from the PDEGym benchmark and show that TTC captures improved predictions relative to standard non-adaptive auto-regressive inference. This TTC framework marks a foundational step towards more advanced reasoning algorithms or PDE modeling, inluding building reinforcement-learning-based approaches, potentially transforming computational workflows in physics and engineering.

James Amarel, Nicolas Hengartner, Robyn Miller et al.

Foundation models trained as autoregressive PDE surrogates hold significant promise for accelerating scientific discovery through their capacity to both extrapolate beyond training regimes and efficiently adapt to downstream tasks despite a paucity of examples for fine-tuning. However, reliably achieving genuine generalization - a necessary capability for producing novel scientific insights and robustly performing during deployment - remains a critical challenge. Establishing whether or not these requirements are met demands evaluation metrics capable of clearly distinguishing genuine model generalization from mere memorization. We apply the influence function formalism to systematically characterize how autoregressive PDE surrogates assimilate and propagate information derived from diverse physical scenarios, revealing fundamental limitations of standard models and training routines in addition to providing actionable insights regarding the design of improved surrogates.

Benjamin Migliori, Riley Zeller-Townson, Daniel Grady et al.

Automatic modulation classification (AMC) is an important task for modern communication systems; however, it is a challenging problem when signal features and precise models for generating each modulation may be unknown. We present a new biologically-inspired AMC method without the need for models or manually specified features --- thus removing the requirement for expert prior knowledge. We accomplish this task using regularized stacked sparse denoising autoencoders (SSDAs). Our method selects efficient classification features directly from raw in-phase/quadrature (I/Q) radio signals in an unsupervised manner. These features are then used to construct higher-complexity abstract features which can be used for automatic modulation classification. We demonstrate this process using a dataset generated with a software defined radio, consisting of random input bits encoded in 100-sample segments of various common digital radio modulations. Our results show correct classification rates of > 99% at 7.5 dB signal-to-noise ratio (SNR) and > 92% at 0 dB SNR in a 6-way classification test. Our experiments demonstrate a dramatically new and broadly applicable mechanism for performing AMC and related tasks without the need for expert-defined or modulation-specific signal information.