Classical constitutive modeling of path-dependent inelastic materials relies on internal state variables whose evolution equations must be postulated based on domain knowledge and calibrated against experimental data. However, in many practical settings, the relevant internal variables are typically not measurable in experiments, and the constitutive response must be inferred entirely from measured strain-stress data without any prior knowledge of the material's internal state. We propose a data-driven constitutive modeling framework based on the concept of a material operator, which treats a deforming material as a functional mapping from its entire strain history to the corresponding stress response. In contrast to traditional autoregressive or recurrent formulations, the model is trained directly on full loading paths as function-to-function mappings, predicting complete stress trajectories in a single parallel forward pass. Temporal path dependence is enforced through a causally masked attention mechanism embedded within the operator, which restricts the model's attention to past material states while preserving computational parallelizability. Spectral convolutions provide discretization-invariant representations in the frequency domain, while causal attention captures highly adaptive, non-local history dependence. Furthermore, sinusoidal activation functions are used to resolve the strong nonlinear transitions inherent in inelastic regimes. The framework is evaluated across multidimensional, rate-independent material models exhibiting complex phenomena, with an emphasis on nonlinear plasticity and ductile damage accumulation. The results demonstrate accurate and robust predictions of irreversible deformation mechanisms while simultaneously achieving resolution invariance and excellent parallel efficiency.
Context: Software startups are newly created companies with no operating history and fast in producing cutting-edge technologies. These companies develop software under highly uncertain conditions, tackling fast-growing markets under severe lack of resources. Therefore, software startups present a unique combination of characteristics which pose several challenges to software development activities. Objective: This study aims to structure and analyze the literature on software development in startup companies, determining thereby the potential for technology transfer and identifying software development work practices reported by practitioners and researchers. Method: We conducted a systematic mapping study, developing a classification schema, ranking the selected primary studies according their rigor and relevance, and analyzing reported software development work practices in startups. Results: A total of 43 primary studies were identified and mapped, synthesizing the available evidence on software development in startups. Only 16 studies are entirely dedicated to software development in startups, of which 10 result in a weak contribution (advice and implications (6); lesson learned (3); tool (1)). Nineteen studies focus on managerial and organizational factors. Moreover, only 9 studies exhibit high scientific rigor and relevance. From the reviewed primary studies, 213 software engineering work practices were extracted, categorized and analyzed. Conclusion: This mapping study provides the first systematic exploration of the state-of-art on software startup research. The existing body of knowledge is limited to a few high quality studies. Furthermore, the results indicate that software engineering work practices are chosen opportunistically, adapted and configured to provide value under the constrains imposed by the startup context.
Nicolò Paternoster, Carmine Giardino, M. Unterkalmsteiner et al.· Information and Software Tec...· 394 citations· ⚡54
Software startups are newly created companies with little operating history and oriented towards producing cutting-edge products. As their time and resources are extremely scarce, and one failed project can put them out of business, startups need effective practices to face with those unique challenges. However, only few scientific studies attempt to address characteristics of failure, especially during the early-stage. With this study we aim to raise our understanding of the failure of early-stage software startup companies. This state-of-practice investigation was performed using a literature review followed by a multiple-case study approach. The results present how inconsistency between managerial strategies and execution can lead to failure by means of a behavioral framework. Despite strategies reveal the first need to understand the problem/solution fit, actual executions prioritize the development of the product to launch on the market as quickly as possible to verify product/market fit, neglecting the necessary learning process.
Carmine Giardino, Xiaofeng Wang, P. Abrahamsson· International Conference on...· 175 citations· ⚡19
In the context of software startups, project failure is embraced actively and considered crucial to obtain validated learning that can lead to pivots. A pivot is the strategic change of a business concept, product or the different elements of a business model. A better understanding is needed on different types of pivots and different factors that lead to failures and trigger pivots, for software entrepreneurial teams to make better decisions under chaotic and unpredictable environment. Due to the nascent nature of the topic, the existing research and knowledge on the pivots of software startups are very limited. In this study, we aimed at identifying the major types of pivots that software startups make during their startup processes, and highlighting the factors that fail software projects and trigger pivots. To achieve this, we conducted a case survey study based on the secondary data of the major pivots happened in 49 software startups. 10 pivot types and 14 triggering factors were identified. The findings show that customer need pivot is the most common among all pivot types. Together with customer segment pivot, they are common market related pivots. The major product related pivots are zoom-in and technology pivots. Several new pivot types were identified, including market zoom-in, complete and side project pivots. Our study also demonstrates that negative customer reaction and flawed business model are the most common factors that trigger pivots in software startups. Our study extends the research knowledge on software startup pivot types and pivot triggering factors. Meanwhile it provides practical knowledge to software startups, which they can utilize to guide their effective decisions on pivoting.
Sohaib Shahid Bajwa, Xiaofeng Wang, Anh Nguyen-Duc et al.· Empirical Software Engineeri...· 127 citations· ⚡15
Minimum viable product (MVP) is the main focus of both business and product development activities in software startups. We empirically explored five early stage software startups to understand how MVP are used in early stages. Data was collected from interviews, observation and documents. We looked at the MVP usage from two angles, software prototyping and boundary spanning theory. We found that roles of MVPs in startups were not fully aware by entrepreneurs. Besides supporting validated learning, MVPs are used to facilitate product design, to bridge communication gaps and to facilitate cost-effective product development activities. Entrepreneurs should consider a systematic approach to fully explore the value of MVP, as a multiple facet product (MFP). The work also implies several research directions about prototyping practices and patterns in software startups.
Anh Nguyen-Duc, P. Abrahamsson· International Conference on...· 92 citations· ⚡9
This article investigates several physics-informed and hybrid machine learning strategies that incorporate physics knowledge in experimental data-driven deep-learning models for predicting the bond quality and porosity of fused filament fabrication (FFF) parts. Three types of strategies are explored to incorporate physics constraints and multi-physics FFF simulation results into a deep neural network (DNN), thus ensuring consistency with physical laws: (1) incorporate physics constraints within the loss function of the DNN, (2) use physics model outputs as additional inputs to the DNN model, and (3) pre-train a DNN model with physics model input-output and then update it with experimental data. These strategies help to enforce a physically consistent relationship between bond quality and tensile strength, thus making porosity predictions physically meaningful. Eight different combinations of the above strategies are investigated. The results show how the combination of multiple strategies produces accurate machine learning models even with limited experimental data.
B. Kapusuzoglu, S. Mahadevan· JOM· 79 citations· ⚡2
Amortized sampling of the posterior over data is studied, and the asymptotic correctness of a data-free learning objective, relative trajectory balance, is proved for training a diffusion model that samples from this posterior, a problem that existing methods solve only approximately or in restricted cases.
S. Venkatraman, Moksh Jain, Luca Scimeca et al.· Neural Information Processin...· 75 citations· ⚡5
A new machine-learning framework aims to improve the success rate of computational protein design while moving away from results that reproduce sequences found in nature.
MIT News · Artificial Intelligence· news.mit.eduAug 24, 2026
