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Earth System Models (ESMs) are critical for understanding past climates and projecting future scenarios. However, the complexity of these models, which include large code bases, a wide community of developers, and diverse computational platforms, poses significant challenges for software quality assurance. The increasing adoption of GPUs and heterogeneous architectures further complicates verification efforts. Traditional verification methods often rely on bitwise reproducibility, which is not always feasible, particularly under new compilers or hardware. Manual expert evaluation, on the other hand, is subjective and time-consuming. Formal methods offer a mathematically rigorous alternative, yet their application in ESM development has been limited due to the lack of climate model-specific representations and tools. Here, we advocate for the broader adoption of formal methods in climate modeling. In particular, we identify key aspects of ESMs that are well suited to formal specification and introduce abstraction approaches for a tailored framework. To demonstrate this approach, we present a case study using CIVL model checker to formally verify a bug fix in an ocean mixing parameterization scheme. Our goal is to develop accessible, domain-specific formal tools that enhance model confidence and support more efficient and reliable ESM development. 

Many recent computational accelerators provide non-standard (e.g., reduced precision) arithmetic operations to enhance performance for floating-point matrix multiplication. Unfortunately, the properties of these accelerators are not widely understood and lack sufficient descriptions of their behavior. This makes it difficult for tool builders beyond the original vendor to target or simulate the hardware correctly, or for algorithm designers to be confident in their code. To address these gaps, prior studies have probed the behavior of these units with manually crafted tests. Such tests are cumbersome to design, and adapting them as the accelerators evolve requires repeated manual effort. We present a formal model for the tensor cores of NVIDIA’s Volta, Turing, and Ampere GPUs. We identify specific properties—rounding mode, precision, and accumulation order—that drive these cores’ behavior. We formalize these properties and then use the formalization to automatically generate discriminating inputs that illustrate differences among machines. Our results confirm many of the findings of previous tensor core studies, but also identify subtle disagreements. In particular, NVIDIA’s machines do not, as previously reported, use round-to-zero for accumulation, and their 5-term accumulator requires 3 extra carry-out bits for full accuracy. Using our formal model, we analyze two existing algorithms that use half-precision tensor cores to accelerate single-precision multiplication with error correction. Our analysis reveals that the newer algorithm, designed to be more accurate than the first, is actually less accurate for certain inputs. 

Theorem proving demonstrates promising potential for verifying problems beyond the capabilities of SMT-solver-based verification tools. We explore and showcase the capability of Lean, an increasingly popular theorem-proving tool, in deriving the error bounds of table-based Logarithmic Number Systems (LNS). LNS reduces the number of bits needed to represent a high dynamic range of real numbers with finite precision and efficiently performs multiplication and division. However, in LNS, addition and subtraction become non-linear functions that must be approximated—typically using precomputed look-up tables. We provide the first rigorous analysis of LNS that covers first-order Taylor approximation, cotransformation techniques inspired by European Logarithmic Microprocessor, and the errors introduced by fixed-point arithmetic involved in LNS implementations. By analyzing all error sources and deriving symbolic error bounds for each, then accumulating these to obtain the final error bound, we prove the correctness of these bounds using Lean and its Mathlib library. We empirically validate our analysis using an exhaustive Python implementation, demonstrating that our analytical interpolation bounds are tight, and our analytical cotransformation bounds overestimate between one and two bits. 

Error-bounded lossy compression has been a critical technique to significantly reduce the sheer amounts of simulation datasets for high-performance computing (HPC) scientific applications while effectively controlling the data distortion based on user-specified error bound. In many real-world use cases, users must perform computational operations on the compressed data. However, none of the existing error-bounded lossy compressors support operations, inevitably resulting in undesired decompression costs. In this paper, we propose a novel error-bounded lossy compressor (called SZOps), which supports not only error-bounding features but efficient computations (including negation, scalar addition, scalar multiplication, mean, variance, etc.) on the compressed data without the complete decompression step, which is the first attempt to the best of our knowledge. We develop several optimization strategies to maximize the overall compression ratio and execution performance. We evaluate SZOps compared to other state-of-the-art lossy compressors based on multiple real-world scientific application datasets. 

Abstract Recent demand for distributed software had led to a surge in popularity in actor‐based frameworks. However, even with the stylized message passing model of actors, writing correct distributed software is still difficult. We present our work on linearizability checking in DS2, an integrated framework for specifying, synthesizing, and testing distributed actor systems. The key insight of our approach is that often subcomponents of distributed actor systems represent common algorithms or data structures (e.g., a distributed hash table or tree) that can be validated against a simple sequential model of the system. This makes it easy for developers to validate their concurrent actor systems without complex specifications. DS2 automatically explores the concurrent schedules that system could arrive at, and it compares observed output of the system to ensure it is equivalent to what the sequential implementation could have produced. We describe DS2's linearizability checking and test it on several concurrent replication algorithms from the literature. We explore in detail how different algorithms for enumerating the model schedule space fare in finding bugs in actor systems, and we present our own refinements on algorithms for exploring actor system schedules that we show are effective in finding bugs.