Over the last decade, widely publicized AI breakthroughs have disrupted various areas of science and technology. Many of the most credible and transformative advances have followed a “common task framework” (CTF) paradigm, in which a clearly specified machine learning task is shared with a research community through standardized datasets, baseline algorithms, and evaluation metrics. Within this framework, researchers compete to improve performance, enabling rapid identification and adoption of superior methods. Despite its success, the CTF paradigm is not yet universal. Some fields lack standardized benchmarks, shared code and data, or consistent evaluation practices, leading to fragmented progress and difficulty comparing claims. Fields that have embraced CTFs repeatedly demonstrate accelerated and verifiable improvement. We argue that dynamic systems research is ready to adopt this approach. We introduce CTF4Science, a framework for defining tasks, publishing datasets and benchmarks, and tracking performance across prediction, denoising, and parameter extrapolation problems.
Artificial Intelligence and Machine Learning have become central tools in scientific and engineering computation. Their adoption has accelerated across physics, materials science, structural engineering, thermal modeling, and control systems. Despite these benefits, the use of Artificial Intelligence introduces nondeterministic behavior that conflicts with longstanding expectations of reproducibility, traceability, and predictable numerical performance. Regulatory frameworks in medicine, aerospace, automotive safety, and nuclear engineering require deterministic computation for verification and certification [1], [2], [3]. This article examines the controversies that arise when Artificial Intelligence is applied to scientific and engineering workflows. It analyzes the sources of nondeterminism in hardware, software, and models. It presents the Mediated Deterministic Architecture (MDA) as the primary engineering contribution of this work, an architecture that constrains nondeterministic components behind deterministic validation layers governed by three design principles, independence, directional sensitivity, and extrapolation awareness, and provides a precise guarantee: every output the system emits satisfies an explicit set of physical invariants, by independent validation or by certified fallback. The article evaluates the implications of these controversies and outlines future directions for responsible integration of Artificial Intelligence into high assurance computation.
We examine super-resolution models, which predict system state at high resolutions given coarse resolution information, and hold great potential for multi-scale scientific applications. We classify existing models into implicit and explicit super-resolution models, and consider their theoretical underpinnings and state-of-practice from a spectral viewpoint. For implicit (zero-shot) models we identify a fallacy in their claim of generality; they require data or prior knowledge of interactions between scales for predictions to be unique. Explicit models, such as those used for turbulence, have issues with spectral bias, affecting predictions of fine-scale energy. While a few recent works have proposed remedies for spectral bias, we contend that capturing total energy is a necessary, but not sufficient condition, for accuracy. To accurately describe fine scales, models must also preserve local isotropy and physics invariants.
Motivated by the ongoing debate over whether physics-informed neural networks (PINNs) can serve as universal solvers for partial differential equations (PDEs), this paper uses elliptic PDEs as a concrete setting to describe a family of physics-preserving neural network (P2NN) methods. Beyond being physics-informed, P2NN methods are designed to preserve the underlying physical principles which are often violated by PINNs. Specifically, P2NN methods employ neural networks as approximating functions, an equivalent formulation of the governing PDEs, and physics-preserving numerical differentiation operators. For diffusion-reaction equations, the Ritz and the dual formulations, associated with the primal and dual variables respectively, provide natural optimization principles and hence preserve physics. For convection-diffusion-reaction equations, we examine the Bramble-Schatz and firstorder system least-squares (LS) formulations and assess their applicability. Finally, we emphasize that a viable NN-based method also hinges on accurate numerical integration and physics-preserving numerical differentiation. These components are essential, nontrivial, and are discussed within the proposed P2NN framework.
This study presents a review of Mapper in applications for patient stratification. We identify successes and shortcomings of Mapper applications and connect these to problems in ML for science more broadly.
