An official website of the United States government
Problem solving is an essential part of engineering. Research shows that students are not exposed to ill-structured problems in the engineering classrooms as much as well-structured problems and do not feel as confident and comfortable solving them. There have been several studies on how engineering students solve and perceive ill-structured problems, however, understanding engineering faculty’s perceptions of teaching and solving such problems is important as well. Since it is the engineering faculty who teach students how to approach engineering problems, it is essential to understand how they perceive solving and teaching of these problems. The following research question has guided this research: What beliefs do engineering faculty have about teaching and solving ill-structured problems? Ten tenure-track or tenured faculty in civil engineering from various universities across the U.S. were interviewed after solving an ill-structured engineering problem. Their responses were transcribed and coded. The findings suggest that faculty generally preferred to teach both well-structured and ill-structured problems in their courses. They also acknowledge the advantages of ill-structured problems, in that they promote critical thinking, require creativity, and are more challenging. However, the results showed that some are less likely to use ill-structured problems in their teaching compared to well-structured problems. We also found that faculty became more comfortable teaching ill-structured problems as they gain more experience in teaching these types of problems. Faculty’s responses showed that while they solve ill-structured problems as part of their research on a regular basis, some faculty do not integrate these problems in the classes that they teach. These results indicate that although faculty recognize the importance of using ill-structured problems while teaching, the lack of experience with teaching these problems, other faculty responsibilities, and the complex nature of these problems make it challenging for engineering faculty to incorporate these problems into the engineering classroom. Based on these findings, in order to improve faculty’s comfort and willingness to use ill-structured problems in their teaching, recommendations for faculty are provided in the paper.
more »
« less
Optimization hardness constrains ecological transients
Living systems operate far from equilibrium, yet few general frameworks provide global bounds on biological transients. In high-dimensional biological networks like ecosystems, long transients arise from the separate timescales of interactions within versus among subcommunities. Here, we use tools from computational complexity theory to frame equilibration in complex ecosystems as the process of solving an analogue optimization problem. We show that functional redundancies among species in an ecosystem produce difficult, ill-conditioned problems, which physically manifest as transient chaos. We find that the recent success of dimensionality reduction methods in describing ecological dynamics arises due to preconditioning, in which fast relaxation decouples from slow solving timescales. In evolutionary simulations, we show that selection for steady-state species diversity produces ill-conditioning, an effect quantifiable using scaling relations originally derived for numerical analysis of complex optimization problems. Our results demonstrate the physical toll of computational constraints on biological dynamics.
more »
« less
- PAR ID:
- 10661477
- Editor(s):
- Moreno, Yamir
- Publisher / Repository:
- Public Library of Science
- Date Published:
- Journal Name:
- PLOS Computational Biology
- Volume:
- 21
- Issue:
- 5
- ISSN:
- 1553-7358
- Page Range / eLocation ID:
- e1013051
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Workplace engineering problems are different from the problems that undergraduate engineering students typically encounter in most classroom settings. Students are most commonly given well-structured problems which have clear solution paths along with well-defined constraints and goals. This paper reports on research that examines how undergraduate engineering students perceived solving an ill-structured problem. Eighteen undergraduate civil engineering students were asked to solve an ill-structured engineering problem, and were interviewed after they completed solving the problem. This qualitative study is guided by the following research question: What factors do students perceive to influence their solving of an ill-structured civil engineering problem? Students’ responses to seven follow-up interview questions were transcribed and reviewed by research team members, which were used to develop codes and themes associated with these responses. Students’ transcripts were then coded following the developed codes. The analysis of data revealed that students were generally aware of the main positives and negatives of their proposed solutions to the ill-structured problem and reported that their creativity influenced their solutions and problem solving processes. Student responses also indicated that specific life events such as classes that they had taken, personal experiences, and exposure to other ill-structured problems during an internship helped them develop their proposed solution. Given students’ responses and overall findings, this supports creating learning environments for engineering students where they can support increasing their creativity and be more exposed to complex engineering problems.more » « less
-
Deep neural networks (DNNs) have shown their success as high-dimensional function approximators in many applications; however, training DNNs can be challenging in general. DNN training is commonly phrased as a stochastic optimization problem whose challenges include non-convexity, non-smoothness, insufficient regularization, and complicated data distributions. Hence, the performance of DNNs on a given task depends crucially on tuning hyperparameters, especially learning rates and regularization parameters. In the absence of theoretical guidelines or prior experience on similar tasks, this requires solving many training problems, which can be time-consuming and demanding on computational resources. This can limit the applicability of DNNs to problems with non-standard, complex, and scarce datasets, e.g., those arising in many scientific applications. To remedy the challenges of DNN training, we propose slimTrain, a stochastic optimization method for training DNNs with reduced sensitivity to the choice hyperparameters and fast initial convergence. The central idea of slimTrain is to exploit the separability inherent in many DNN architectures; that is, we separate the DNN into a nonlinear feature extractor followed by a linear model. This separability allows us to leverage recent advances made for solving large-scale, linear, ill-posed inverse problems. Crucially, for the linear weights, slimTrain does not require a learning rate and automatically adapts the regularization parameter. Since our method operates on mini-batches, its computational overhead per iteration is modest. In our numerical experiments, slimTrain outperforms existing DNN training methods with the recommended hyperparameter settings and reduces the sensitivity of DNN training to the remaining hyperparameters.more » « less
-
null (Ed.)Ecohydrological phenomena are o ften multiscale in nature, with behavioTur that emerges from the interaction of tightly coupled systems having characteristic timescales that differ by orders of magnitude. Models address these differences using timescale separation methods, where each system is held in psuedo‐steady state while the other evolves. When the computational demands of solving the ‘fast’ system are large, this strategy can become numerically intractable. Here, we use emulation modelling to accelerate the simulation of a computationally intensive ‘fast’ system: overland flow. We focus on dryland ecosystems in which storms generate overland flow, on timescales of 101 − 2 s. In these ecosystems, overland flow delivers crucial water inputs to vegetation, which grows and disperses ‘slowly’, on timescales of 107 − 9 s. Emulation allows for a physically realistic treatment of flow, advancing on phenomenological descriptions used in previous studies. Resolving the within‐storm processes reveals novel dynamics, including new transition pathways from patchy vegetation to desertification, that are specifically controlled by storm processes.more » « less
-
null (Ed.)Abstract— In this Work in Progress Research paper, we present preliminary results on the analysis of the problems present in a common engineering textbook. In order to transition students from novice to expert problem solving, they must have practice solving problems that are typical of engineering practice, i.e. illstructured and complex. While it is generally believed that classroom problems are for the most part closed-ended and not complex, there is no work in the literature to confirm this belief. In order to address this gap, we analyzed the types of problems present in a commonly used statics textbook, using Jonassen’s well-known typology. Our findings show that almost all of the problems are algorithmic, with a few rule-based and story problems. There were no problems with higher levels of illstructuredness, such as decision-making, diagnosis-solution, or design problems. Some educators may believe that because statics is an introductory level class, it is appropriate to only present wellstructured problems. We argue that it is both possible and necessary to include ill-structured problems in classes at all levels. Doing so could potentially support students’ critical transition from novice to expert problem solvers. Keywords—problem-solving, statics, ambiguitymore » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1371/journal.pcbi.1013051
