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Mathematical modeling is typically framed as the art of reductionism of scientific knowledge into an arithmetical layout. However, most untrained people get the art of modeling wrong and end up neglecting it because modeling is not simply about writing equations and generating numbers through simulations. Models tell not only about a story; they are spoken to by the circumstances under which they are envisioned. They guide apprentice and experienced modelers to build better models by preventing known pitfalls and invalid assumptions in the virtual world and, most importantly, learn from them through simulation and identify gaps in pushing scientific knowledge further. The power of the human mind is well-documented for idealizing concepts and creating virtual reality models, and as our hypotheses grow more complicated and more complex data become available, modeling earns more noticeable footing in biological sciences. The fundamental modeling paradigms include discrete-events, dynamic systems, agent-based (AB), and system dynamics (SD). The source of knowledge is the most critical step in the model-building process regardless of the paradigm, and the necessary expertise includes (a) clear and concise mental concepts acquired through different ways that provide the fundamental structure and expected behaviors of the model and (b) numerical data necessary for statistical analysis, not for building the model. The unreasonable effectiveness of models to grow scientific learning and knowledge in sciences arise because different researchers would model the same problem differently, given their knowledge and experiential background, leading to choosing different variables and model structures. Secondly, different researchers might use different paradigms and even unalike mathematics to resolve the same problem; thus, model needs are intrinsic to their perceived assumptions and structures. Thirdly, models evolve as the scientific community knowledge accumulates and matures over time, hopefully resulting in improved modeling efforts; thus, the perfect model is fictional. Some paradigms are most appropriate for macro, high abstraction with less detailed-oriented scenarios, while others are most suitable for micro, low abstraction with higher detailed-oriented strategies. Modern hybridization aggregating artificial intelligence (AI) to mathematical models can become the next technological wave in modeling. AI can be an integral part of the SD/AB models and, before long, write the model code by itself. Success and failures in model building are more related to the ability of the researcher to interpret the data and understand the underlying principles and mechanisms to formulate the correct relationship among variables rather than profound mathematical knowledge.
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Stored only when both papers are in the corpus — 28 citations exist upstream.
Papers that cite the same references — the relational fallback while embeddings are still backfilling.
Imported from OpenAlex (CC0) — nothing here is generated.