N M Anoop Krishnan

Karn Tiwari, N M Anoop Krishnan, Prathosh A P

Neural operators extend data-driven models to map between infinite-dimensional functional spaces. These models have successfully solved continuous dynamical systems represented by differential equations, viz weather forecasting, fluid flow, or solid mechanics. However, the existing operators still rely on real space, thereby losing rich representations potentially captured in the complex space by functional transforms. In this paper, we introduce a Complex Neural Operator (CoNO), that parameterizes the integral kernel in the complex fractional Fourier domain. Additionally, the model employing a complex-valued neural network along with aliasing-free activation functions preserves the complex values and complex algebraic properties, thereby enabling improved representation, robustness to noise, and generalization. We show that the model effectively captures the underlying partial differential equation with a single complex fractional Fourier transform. We perform an extensive empirical evaluation of CoNO on several datasets and additional tasks such as zero-shot super-resolution, evaluation of out-of-distribution data, data efficiency, and robustness to noise. CoNO exhibits comparable or superior performance to all the state-of-the-art models in these tasks. Altogether, CoNO presents a robust and superior model for modeling continuous dynamical systems, providing a fillip to scientific machine learning.

Magdalena Lederbauer, Siddharth Betala, Xiyao Li et al.

The development of synthesis procedures remains a fundamental challenge in materials discovery, with procedural knowledge scattered across decades of scientific literature in unstructured formats that are challenging for systematic analysis. In this paper, we propose a multi-modal toolbox that employs large language models (LLMs) and vision language models (VLMs) to automatically extract and organize synthesis procedures and performance data from materials science publications, covering text and figures. We curated 81k open-access papers, yielding LeMat-Synth (v 1.0): a dataset containing synthesis procedures spanning 35 synthesis methods and 16 material classes, structured according to an ontology specific to materials science. The extraction quality is rigorously evaluated on a subset of 2.5k synthesis procedures through a combination of expert annotations and a scalable LLM-as-a-judge framework. Beyond the dataset, we release a modular, open-source software library designed to support community-driven extension to new corpora and synthesis domains. Altogether, this work provides an extensible infrastructure to transform unstructured literature into machine-readable information. This lays the groundwork for predictive modeling of synthesis procedures as well as modeling synthesis--structure--property relationships.

Sajid Mannan, Vaibhav Bihani, Carmelo Gonzales et al.

Universal machine learning force fields (UMLFFs) promise to revolutionize materials science by enabling rapid atomistic simulations across the periodic table. However, their evaluation has been limited to computational benchmarks that may not reflect real-world performance. Here, we present UniFFBench, a comprehensive framework for evaluating UMLFFs against experimental measurements of ~1,500 carefully curated mineral structures spanning diverse chemical environments, bonding types, structural complexity, and elastic properties. Our systematic evaluation of six state-of-the-art UMLFFs reveals a substantial reality gap: models achieving impressive performance on computational benchmarks often fail when confronted with experimental complexity. Even the best-performing models exhibit higher density prediction error than the threshold required for practical applications. Most strikingly, we observe disconnects between simulation stability and mechanical property accuracy, with prediction errors correlating with training data representation rather than the modeling method. These findings demonstrate that while current computational benchmarks provide valuable controlled comparisons, they may overestimate model reliability when extrapolated to experimentally complex chemical spaces. Altogether, UniFFBench establishes essential experimental validation standards and reveals systematic limitations that must be addressed to achieve truly universal force field capabilities.

Karn Tiwari, Niladri Dutta, N M Anoop Krishnan et al.

Neural operators have emerged as powerful data-driven frameworks for solving Partial Differential Equations (PDEs), offering significant speedups over numerical methods. However, existing neural operators struggle with scalability in high-dimensional spaces, incur high computational costs, and face challenges in capturing continuous and long-range dependencies in PDE dynamics. To address these limitations, we introduce the Latent Mamba Operator (LaMO), which integrates the efficiency of state-space models (SSMs) in latent space with the expressive power of kernel integral formulations in neural operators. We also establish a theoretical connection between state-space models (SSMs) and the kernel integral of neural operators. Extensive experiments across diverse PDE benchmarks on regular grids, structured meshes, and point clouds covering solid and fluid physics datasets, LaMOs achieve consistent state-of-the-art (SOTA) performance, with a 32.3% improvement over existing baselines in solution operator approximation, highlighting its efficacy in modeling complex PDE solutions.

Karn Tiwari, N M Anoop Krishnan, A P Prathosh

Neural operators extend data-driven models to map between infinite-dimensional functional spaces. While these operators perform effectively in either the time or frequency domain, their performance may be limited when applied to non-stationary spatial or temporal signals whose frequency characteristics change with time. Here, we introduce Complex Neural Operator (CoNO) that parameterizes the integral kernel using Fractional Fourier Transform (FrFT), better representing non-stationary signals in a complex-valued domain. Theoretically, we prove the universal approximation capability of CoNO. We perform an extensive empirical evaluation of CoNO on seven challenging partial differential equations (PDEs), including regular grids, structured meshes, and point clouds. Empirically, CoNO consistently attains state-of-the-art performance, showcasing an average relative gain of 10.9%. Further, CoNO exhibits superior performance, outperforming all other models in additional tasks such as zero-shot super-resolution and robustness to noise. CoNO also exhibits the ability to learn from small amounts of data -- giving the same performance as the next best model with just 60% of the training data. Altogether, CoNO presents a robust and superior model for modeling continuous dynamical systems, providing a fillip to scientific machine learning.